diff --git a/Outils.rtf b/Outils.rtf new file mode 100644 index 0000000..3fbed34 --- /dev/null +++ b/Outils.rtf @@ -0,0 +1,21 @@ +{\rtf1\ansi\ansicpg1252\cocoartf1038\cocoasubrtf360 +{\fonttbl\f0\fswiss\fcharset0 Helvetica;\f1\fmodern\fcharset0 Courier;} +{\colortbl;\red255\green255\blue255;} +\paperw11900\paperh16840\margl1440\margr1440\vieww9000\viewh8400\viewkind0 +\pard\tx566\tx1133\tx1700\tx2267\tx2834\tx3401\tx3968\tx4535\tx5102\tx5669\tx6236\tx6803\ql\qnatural\pardirnatural + +\f0\fs24 \cf0 Outils SVN : \ +CREATION : http://ensiwiki.ensimag.fr/index.php/Tuto_cr\'e9er_son_propre_d\'e9p\'f4t_SVN\ +\ +// pour le commit\ +\pard\pardeftab720\ql\qnatural + +\f1\fs26 \cf0 svn commit -m "explication de la modif" src/Test.java\ +\ +l'adresse du d\'e9p\'f4t est dans .svn/entries.\ +\ +Mode commande sous vim ":"\ +entree : q enter\ +\ +Gestion de projet svn : http://www.lifl.fr/~durif/svn/svn.html\ +} \ No newline at end of file diff --git a/TAGS b/TAGS new file mode 100644 index 0000000..32f1e9e --- /dev/null +++ b/TAGS @@ -0,0 +1,2692 @@ + +actions.c,671 +static Plist Given_rules 31,1101 +static Plist Generated_rules 32,1138 +static Plist Kept_rules 33,1175 +static Plist Level_rules 34,1212 +#define NN 47,1692 +static char *Changable_flags[51,1805 +static char *Changable_parms[57,1911 +static char *Changable_flags_rebuild[75,2377 +static char *Changable_parms_rebuild[80,2488 +BOOL changable_flag(109,2976 +BOOL changable_parm(124,3235 +BOOL changable_flag_rebuild(139,3477 +BOOL changable_parm_rebuild(154,3768 +void init_action(175,4169 +void init_actions(210,5012 +void register_action(242,5700 +BOOL apply_action(283,6788 +void statistic_actions(336,8237 +void proof_action(383,9428 +void actions_in_proof(420,10253 + +autosketches4.c,86 +#define PROVER_NAME 19,755 +void attach_sketch_hint_labels(34,1043 +int main(54,1542 + +demodulate.c,392 +static Mindex Demod_idx;26,885 +static Mindex Back_demod_idx;27,910 +void init_demodulator_index(39,1043 +void init_back_demod_index(54,1308 +void index_demodulator(69,1572 +void index_back_demod(86,1867 +void destroy_demodulation_index(105,2208 +void destroy_back_demod_index(121,2438 +void demodulate_clause(140,2835 +Plist back_demodulatable(188,4139 +void back_demod_idx_report(203,4416 + +fof-prover9.c,45 +#define PROVER_NAME 19,755 +int main(31,954 + +foffer.c,119 +Formula construct_problem(30,911 +Formula reduce_problem(80,2008 +Plist foffer_clausify(100,2540 +int foffer(127,3154 + +forward_subsume.c,287 +static Di_tree Nonunit_index;26,859 +static Lindex Unit_index;27,889 +#define NUM_INDEXES 29,921 +static Lindex Idx[30,964 +void init_fsub_index(43,1099 +void fsub_destroy_index(70,1648 +void index_fsub(94,1981 +Topform forward_subsumption_old(130,2719 +void unit_deletion_old(159,3328 + +giv_select.c,1408 +enum { GS_ORDER_WEIGHT,26,902 + GS_ORDER_AGE,27,926 + GS_ORDER_RANDOM28,947 +typedef struct giv_select *Giv_select;Giv_select31,987 +struct giv_select giv_select33,1027 +typedef struct select_state *Select_state;Select_state43,1340 +static struct select_state select_state47,1408 +} High,53,1655 +} High, Low;53,1655 +static BOOL Rule_needs_semantics 55,1722 +static int Sos_size 56,1764 +static double Low_water_keep 57,1789 +static double Low_water_displace 58,1829 +static int Sos_deleted 59,1873 +static int Sos_displaced 60,1901 +static BOOL Debug 62,1932 +#define PTRS_GIV_SELECT 68,1989 +static unsigned Giv_select_gets,69,2063 +static unsigned Giv_select_gets, Giv_select_frees;69,2063 +Giv_select get_giv_select(78,2193 +void free_giv_select(92,2399 +int current_cycle_size(105,2587 +void init_giv_select(127,2919 +void update_selectors(192,4821 +void insert_into_sos2(253,6258 +void remove_from_sos2(275,6698 +Giv_select next_selector(289,6905 +BOOL givens_available(324,7572 +Topform get_given_clause2(339,7782 +double iterations_to_selection(371,8418 +double least_iters_to_selection(391,9052 +BOOL sos_keep2(431,10036 +Topform worst_clause_of_priority_group(470,10997 +Topform worst_clause(507,11901 +void sos_displace2(530,12380 +void zap_given_selectors(559,12965 +void selector_report(587,13519 +Term selector_rule_term(635,14870 +Plist selector_rules_from_options(657,15394 + +index_lits.c,484 +static Lindex Unit_fpa_idx;23,817 +static Lindex Nonunit_fpa_idx;24,886 +static Lindex Unit_discrim_idx;26,945 +static Di_tree Nonunit_features_idx;27,1009 +void init_literals_index(39,1176 +void destroy_literals_index(63,1656 +void index_literals(82,2095 +void index_denial(112,2753 +void unit_conflict(131,3155 +void unit_deletion(146,3389 +Plist back_unit_deletable(163,3658 +Topform forward_subsumption(178,3879 +Plist back_subsumption(197,4280 +void lits_idx_report(220,4654 + +iterate4.c,104 +#define PROVER_NAME 19,755 +#define PROVER_VERSION 20,789 +void print_banner(35,1032 +int main(54,1499 + +ladr_to_tptp.c,45 +#define PROVER_NAME 21,777 +int main(30,895 + +mprover.c,70 +#define PROVER_NAME 19,755 +BOOL disprover(38,1137 +int main(82,2063 + +newauto.c,68 +#define PROVER_NAME 25,1002 +int main(39,1258 +int NewAuto(87,2710 + +newsax.c,384 +#define PROVER_NAME 25,1002 +int main(42,1324 +int NewSAX(90,2776 +int NewAuto(155,4671 + expanded_proof 256,8114 + results 261,8315 + list_size 263,8344 + input->hints 268,8565 + expanded_proof 269,8632 + assumption_current 284,9288 + assumptions_in_proof 285,9346 + assumptions_active291,9708 + +pred_elim.c,324 +int rsym_occurrences(30,938 +BOOL arg_check(47,1210 +BOOL eliminable_relation(66,1534 +Ilist eliminable_relations(90,2085 +Plist resolve_on_symbol(113,2641 +Plist gen_given(151,3440 +BOOL subsumed_by_member(170,3796 +Plist incorporate_new_clauses(187,4079 +Plist elim_relation(208,4485 +void predicate_elimination(256,5745 + +prover9.c,45 +#define PROVER_NAME 19,755 +int main(30,906 + +provers.c,320 +static char Help_string[26,873 +struct arg_options arg_options36,1279 +struct arg_options get_command_line_args(54,1632 +void max_megs_exit(108,2768 +void process_command_line_args_1(124,3120 +void process_command_line_args_2(149,3782 +void prover_sig_handler(172,4313 +Prover_input std_prover_init_and_input(202,4923 + +search.c,1895 +static jmp_buf Jump_env;32,967 +static Prover_options Opt;34,1031 +static struct prover_attributes Att;35,1091 +static struct prover_stats Stats;36,1163 +static struct prover_clocks Clocks;37,1226 +} Glob;86,2385 +Prover_options init_prover_options(100,2533 +void init_prover_attributes(468,22749 +int get_attrib_id(492,23485 +void update_stats(517,24000 +void fprint_prover_stats(543,24965 +void fprint_prover_clocks(602,27220 +void fprint_all_stats(635,28058 +char *exit_string(661,28529 +void exit_with_message(690,29333 +void report(730,30182 +void possible_report(758,30744 +void done_with_search(793,31521 +void exit_if_over_limit(807,31863 +BOOL inferences_to_make(826,32313 +void index_clashable(840,32527 +BOOL restricted_denial(856,32822 +void disable_clause(871,33092 +void free_search_memory(932,34739 +void handle_proof_and_maybe_exit(997,36057 +void clause_wt_with_adjustments(1085,38497 +void cl_process_simplify(1137,40225 +void cl_process_keep(1188,41653 +void cl_process_conflict(1219,42672 +void cl_process_new_demod(1231,42989 +BOOL skip_black_white_tests(1261,43873 +BOOL cl_process_delete(1270,44092 +void cl_process(1326,45378 +void back_demod(1390,47218 +void back_unit_deletion(1435,48396 +void back_cac_simplify(1476,49458 +void disable_to_be_disabled(1507,50227 +void limbo_process(1567,51786 +void infer_outside_loop(1687,54972 +void given_infer(1724,56110 +void rebuild_sos_index(1780,57596 +void make_inferences(1807,58387 +Topform orient_input_eq(1894,60972 +void auto_inference(1923,61607 +void auto_process(2010,63951 +void auto_denials(2056,64931 +void init_search(2102,66255 +void index_and_process_initial_clauses(2263,71244 +void fatal_setjmp(2531,79701 +Prover_results collect_prover_results(2545,79940 +void zap_prover_results(2578,80848 +void basic_clause_properties(2604,81579 +Prover_results search(2638,82361 +Prover_results forking_search(2763,86795 + +semantics.c,351 +enum { FALSE_IN_ALL,23,816 + FALSE_IN_SOME24,837 +static Plist Compiled_interps 27,862 +static int Eval_limit 28,900 +static BOOL False_in_all;29,927 +static Clock Eval_clock;30,953 +void init_semantics(44,1164 +BOOL eval_limit_ok(78,2073 +void eval_in_interps(108,2856 +void set_semantics(175,4611 +void update_semantics_new_constant(198,5093 + +tptp_to_ladr.c,76 +#define PROGRAM_NAME 21,787 +void read_tptp_input(31,924 +int main(75,2162 + +unfold.c,603 +struct symdata symdata23,813 +enum {NOT_CHECKED 35,950 +enum {NOT_CHECKED = 0, CHECKING,35,950 +enum {NOT_CHECKED = 0, CHECKING, CHECKED,35,950 +enum {NOT_CHECKED = 0, CHECKING, CHECKED, CYCLE}35,950 +void trace_dependents(38,1008 +Ilist eliminate_cycles(70,1628 +BOOL sym_less_or_equal(96,2144 +Ordertype compare_symbols(116,2492 +Ilist insert_symbol(146,3143 +Ilist order_symbols(165,3543 +Ilist eq_defs(182,3824 +int num_constant_symbols(235,5150 +BOOL constant_check(250,5399 +void unfold_eq_defs(283,6096 +Ilist remove_kb_wt_zero(325,7477 +BOOL fold_eq_defs(351,7878 +BOOL one_unary_def(382,8487 + +utilities.c,764 +void print_memory_stats(33,914 +void fsym_collect(75,1898 +BOOL inverse_axiom(94,2239 +void fsym_report(134,3087 +BOOL inverse_order(176,3937 +void p_sym_list(208,4563 +void symbol_order(228,4865 +Ilist unary_symbols(306,7387 +void auto_kbo_weights(330,7786 +int neg_pos_depth_diff(365,8699 +int neg_pos_wt_diff(387,9111 +int neg_pos_depth_difference(412,9546 +void structure_of_clauses(449,10306 +void p_term_list(543,12518 +int plist_size_of_diff(564,12820 +void structure_of_variables(584,13129 +Ordertype clause_compare_m4(630,14109 +int bogo_ticks(688,15451 +Topform next_negative_clause_3(700,15597 +Topform first_negative_clause(767,16862 +Plist neg_clauses_and_descendants(788,17206 +Plist neg_descendants(849,18780 +void check_constant_sharing(888,19769 + +white_black.c,292 +static Plist White_rules 26,902 +static Plist Black_rules 27,935 +static BOOL Rule_needs_semantics 28,968 +void init_white_black(40,1108 +Term new_rule_int(72,1853 +Term new_rule_double(97,2430 +Plist delete_rules_from_options(125,3059 +BOOL black_tests(162,3977 +BOOL white_tests(186,4396 + +../ladr/ac_redun.c,440 +static Ilist C_symbols 21,778 +static Ilist A1_symbols 22,833 +static Ilist A2_symbols 23,905 +static Ilist AC_symbols 24,977 +BOOL same_top(39,1200 +int commutativity(59,1569 +int associativity(91,2262 +int c_associativity(132,3207 +int associativity3(179,4198 +int associativity4(231,5386 +Ordertype can_compare(272,6474 +Term canon(293,6928 +BOOL cac_redundant_atom(342,7960 +BOOL cac_tautology(387,9107 +BOOL cac_redundancy(425,10067 + +../ladr/accanon.c,142 +void flatten(36,1030 +void right_associate(69,1748 +void ac_canonical2(121,2627 +void ac_canonical(180,4499 +int check_ac_canonical(234,5902 + +../ladr/attrib.c,1700 +struct attribute attribute25,875 +#define MAX_ATTRIBUTE_NAMES 37,1170 +} Attribute_names[43,1482 +static int Next_attribute_name 45,1523 +#define PTRS_ATTRIBUTE 51,1589 +static unsigned Attribute_gets,52,1643 +static unsigned Attribute_gets, Attribute_frees;52,1643 +Attribute get_attribute(61,1769 +void free_attribute(75,1968 +void fprint_attrib_mem(94,2362 +void p_attrib_mem(120,2992 +Attribute_type attribute_type(136,3176 +char *attribute_name(148,3351 +int register_attribute(166,3693 +void declare_term_attribute_inheritable(195,4526 +BOOL inheritable(209,4840 +Attribute set_int_attribute(228,5206 +int get_int_attribute(261,5911 +BOOL exists_attribute(287,6465 +Attribute set_term_attribute(312,6950 +void replace_term_attribute(346,7713 +void replace_int_attribute(378,8531 +Term get_term_attribute(410,9327 +Term get_term_attributes(441,10052 +Attribute set_string_attribute(477,10858 +char *get_string_attribute(512,11717 +BOOL string_attribute_member(542,12414 +void zap_attributes(567,12990 +Attribute delete_attributes(589,13421 +Attribute cat_att(619,14026 +Term build_attr_term(644,14497 +Term attributes_to_term(689,15504 +Attribute cat_attributes(709,15928 +int attribute_name_to_id(732,16387 +Attribute term_to_attributes(762,17061 +Attribute inheritable_att_instances(814,18323 +Attribute copy_attributes(840,18889 +void instantiate_inheritable_attributes(869,19513 +void renumber_vars_attributes(892,20006 +void set_vars_attributes(913,20429 +Plist vars_in_attributes(935,20868 +int label_att(959,21280 +BOOL attributes_contain_variables(982,21725 +Attribute copy_int_attribute(1009,22234 +Attribute copy_string_attribute(1030,22613 +Attribute copy_term_attribute(1051,22993 + +../ladr/avltree.c,964 +struct avl_node avl_node24,832 +static BOOL Debug 31,1046 +#define PTRS_AVL_NODE 37,1103 +static unsigned Avl_node_gets,38,1155 +static unsigned Avl_node_gets, Avl_node_frees;38,1155 +Avl_node get_avl_node(47,1277 +void free_avl_node(61,1468 +void fprint_avltree_mem(80,1859 +void p_avltree_mem(106,2486 +int avl_height(126,2753 +int avl_size(142,2972 +void set_height_and_size(154,3126 +BOOL balance_ok(167,3383 +Avl_node rotate_left(179,3563 +Avl_node rotate_right(198,3893 +Avl_node avl_fix(217,4220 +Avl_node avl_insert(262,5260 +Avl_node remove_and_return_largest(295,6105 +Avl_node remove_and_return_smallest(315,6512 +Avl_node avl_delete(342,7133 +Avl_node avl_lookup(383,8118 +void *avl_find(414,8891 +void *avl_smallest(432,9226 +void *avl_largest(453,9575 +int avl_place(476,10045 +double avl_position(510,10853 +void *avl_nth_item(529,11236 +void *avl_item_at_position(556,11890 +void avl_zap(580,12406 +void avl_check(604,12878 +void p_avl(646,14150 + +../ladr/backdemod.c,234 +void index_term_back_demod(30,890 +void index_clause_back_demod(51,1303 +BOOL rewritable_term(70,1684 +BOOL rewritable_clause(99,2257 +Plist back_demod_linear(129,2996 +BOOL lex_rewritable(149,3404 +Plist back_demod_indexed(177,4113 + +../ladr/banner.c,57 +void print_separator(40,1020 +void print_banner(66,1615 + +../ladr/basic.c,453 +static BOOL Basic_paramodulation 64,2487 +static int Nonbasic_flag 65,2561 +void init_basic_paramod(77,2744 +void set_basic_paramod(95,3090 +BOOL basic_paramod(111,3311 +void mark_term_nonbasic(126,3491 +void mark_all_nonbasic(143,3781 +BOOL nonbasic_term(165,4200 +BOOL basic_term(181,4448 +int nonbasic_flag(196,4627 +Term apply_basic(213,4932 +Term apply_basic_substitute(258,6220 +void clear_all_nonbasic_marks(287,6842 +void p_term_basic(308,7218 + +../ladr/btm.c,1920 +typedef struct ac_match_pos * Ac_match_pos;Ac_match_pos23,810 +typedef struct ac_match_free_vars_pos * Ac_match_free_vars_pos;Ac_match_free_vars_pos24,854 +struct btm_state btm_state26,919 +struct ac_match_pos ac_match_pos47,1586 +struct ac_match_free_vars_pos ac_match_free_vars_pos70,2776 +#define POP 81,3224 +#define BACKTRACK 82,3244 +#define GO 83,3264 +#define SUCCESS 84,3284 +#define FAILURE 85,3304 +#define BIND_BT(BIND_BT89,3378 +#define PTRS_AC_MATCH_POS 101,3681 +static unsigned Ac_match_pos_gets,102,3741 +static unsigned Ac_match_pos_gets, Ac_match_pos_frees;102,3741 +#define PTRS_AC_MATCH_FREE_VARS_POS 104,3797 +static unsigned Ac_match_free_vars_pos_gets,105,3877 +static unsigned Ac_match_free_vars_pos_gets, Ac_match_free_vars_pos_frees;105,3877 +#define PTRS_BTM_STATE 107,3953 +static unsigned Btm_state_gets,108,4007 +static unsigned Btm_state_gets, Btm_state_frees;108,4007 +Ac_match_pos get_ac_match_pos(117,4139 +void free_ac_match_pos(131,4359 +Ac_match_free_vars_pos get_ac_match_free_vars_pos(144,4588 +void free_ac_match_free_vars_pos(158,4878 +Btm_state get_btm_state(171,5131 +void free_btm_state(187,5375 +void fprint_btm_mem(206,5763 +void p_btm_mem(244,7007 +void flatten_mult(265,7447 +int macbv_rec(302,8180 +int match_ac_bound_vars(340,9232 +void set_up_free_vars(382,10517 +void unbind_free_var(442,11941 +int free_var_match(477,12690 +Term build_partial_term(591,15486 +void clear_partial_term(621,16054 +#define GO_FUNCTORS 637,16348 +#define GO_BOUND_VARS 638,16372 +#define GO_FREE_VARS 639,16396 +#define SUCCESS 640,16420 +#define FAILURE 641,16444 +int match_ac(661,16973 +void match_ac_cancel(860,22259 +Btm_state match_bt_backup(888,22838 +Btm_state match_bt_guts(932,23563 +int match_commute(1081,26575 +void p_acm(1134,27766 +void p_btm_state(1177,28734 +Btm_state match_bt_first(1234,30497 +Btm_state match_bt_next(1259,30987 +void match_bt_cancel(1294,31787 + +../ladr/btu.c,1356 +#define MAX_ACU_ARGS 23,810 +typedef struct ac_position * Ac_position;Ac_position25,836 +struct ac_position ac_position27,879 +struct btu_state btu_state45,1792 +#define GO 67,2411 +#define SUCCESS 68,2431 +#define EXHAUSTED 69,2451 +#define FAILURE 70,2471 +#define POP 71,2491 +#define BACKTRACK 72,2511 +#define BIND_BT(BIND_BT76,2598 +#define PTRS_BTU_STATE 88,2836 +static unsigned Btu_state_gets,89,2890 +static unsigned Btu_state_gets, Btu_state_frees;89,2890 +#define PTRS_AC_POSITION 91,2940 +static unsigned Ac_position_gets,92,2998 +static unsigned Ac_position_gets, Ac_position_frees;92,2998 +Btu_state get_btu_state(101,3128 +void free_btu_state(116,3345 +Ac_position get_ac_position(129,3537 +void free_ac_position(143,3750 +void fprint_btu_mem(162,4148 +void p_btu_mem(194,5020 +void p_binding(210,5195 +void flatten_deref(244,6222 +int compare_ncv_context(287,7062 +void sort_ac(345,8378 +void elim_con_context(382,9030 +void ac_mult_context(411,9681 +void ac_prepare(466,10784 +void set_up_basis_terms(514,12013 +int unify_ac(560,13210 +void unify_ac_cancel(897,22343 +void p_ac_position(956,23602 +Btu_state unify_bt_backup(986,24303 +int unify_commute(1040,25430 +Btu_state unify_bt_first(1152,28803 +Btu_state unify_bt_next(1175,29320 +void unify_bt_cancel(1208,30123 +Btu_state unify_bt_guts(1246,30927 +void p_bt_tree(1434,34834 + +../ladr/clash.c,438 +#define PTRS_CLASH 27,841 +static unsigned Clash_gets,28,887 +static unsigned Clash_gets, Clash_frees;28,887 +Clash get_clash(37,997 +void free_clash(51,1168 +void fprint_clash_mem(70,1540 +void p_clash_mem(96,2138 +Clash append_clash(116,2451 +void zap_clash(136,2773 +Literals atom_to_literal(158,3124 +Literals apply_lit(179,3547 +int lit_position(191,3732 +Topform resolve(212,4064 +void clash_recurse(272,5622 +void clash(356,8078 + +../ladr/clause_eval.c,1430 +enum { CL_EVAL_AND,39,1420 + CL_EVAL_OR,40,1440 + CL_EVAL_NOT,41,1459 + CL_EVAL_ALL,42,1479 + CL_EVAL_LESS,44,1500 + CL_EVAL_LESS_EQUAL,45,1521 + CL_EVAL_GREATER,46,1548 + CL_EVAL_GREATER_EQUAL,47,1572 + CL_EVAL_EQUAL,48,1602 + CL_EVAL_POSITIVE,50,1625 + CL_EVAL_NEGATIVE,51,1650 + CL_EVAL_MIXED,52,1675 + CL_EVAL_HINT,54,1698 + CL_EVAL_TRUE,56,1720 + CL_EVAL_FALSE,57,1741 + CL_EVAL_HAS_EQUALITY,59,1764 + CL_EVAL_HORN,60,1793 + CL_EVAL_DEFINITE,61,1814 + CL_EVAL_UNIT,62,1839 + CL_EVAL_INITIAL,64,1861 + CL_EVAL_RESOLVENT,65,1885 + CL_EVAL_UR_RESOLVENT,66,1911 + CL_EVAL_HYPER_RESOLVENT,67,1940 + CL_EVAL_FACTOR,68,1972 + CL_EVAL_PARAMODULANT,69,1995 + CL_EVAL_BACK_DEMODULANT,70,2024 + CL_EVAL_SUBSUMER,71,2056 + CL_EVAL_WEIGHT,73,2082 + CL_EVAL_VARIABLES,74,2105 + CL_EVAL_DEPTH,75,2131 + CL_EVAL_LITERALS,76,2153 + CL_EVAL_LEVEL77,2178 +struct clause_eval clause_eval82,2300 +#define PTRS_EVAL_RULE 94,2608 +static unsigned Clause_eval_gets,95,2682 +static unsigned Clause_eval_gets, Clause_eval_frees;95,2682 +Clause_eval get_clause_eval(104,2816 +void free_clause_eval(118,3027 +void zap_clause_eval_rule(138,3280 +Clause_eval compile_clause_eval_rule(160,3685 +BOOL eval_clause_in_rule(284,7091 +BOOL rule_contains_semantics(384,9884 + +../ladr/clause_misc.c,317 +Clist clist_copy(39,1033 +Clist copy_clauses_to_clist(64,1527 +Clist move_clauses_to_clist(90,2067 +Plist input_clauses(115,2549 +void delete_clause(145,3153 +void delete_clist(169,3732 +Topform copy_clause_ija(199,4222 +Plist copy_clauses_ija(220,4687 +void delete_clauses(244,5109 +void make_clause_basic(264,5419 + +../ladr/clauseid.c,421 +#define CLAUSE_ID_TAB_SIZE 23,815 +static Plist Topform_id_tab[25,850 +static unsigned Topform_id_count 26,903 +int next_clause_id(35,1010 +int clause_ids_assigned(51,1236 +void assign_clause_id(70,1642 +void unassign_clause_id(97,2232 +Topform find_clause_by_id(135,3043 +void fprint_clause_id_tab(161,3524 +void p_clause_id_tab(184,3955 +Plist insert_clause_into_plist(204,4377 +BOOL clause_plist_member(239,5183 + +../ladr/clauses.c,437 +Topform clause_member_plist(38,1022 +Plist intersect_clauses(62,1485 +int max_clause_weight(87,1954 +int max_clause_symbol_count(110,2355 +Plist nonneg_clauses(132,2776 +BOOL all_clauses_horn(155,3173 +BOOL all_clauses_unit(177,3512 +BOOL all_clauses_positive(199,3855 +int neg_nonunit_clauses(221,4219 +int negative_clauses(244,4615 +int most_literals(268,4988 +BOOL pos_equality_in_clauses(291,5389 +BOOL equality_in_clauses(315,5835 + +../ladr/clausify.c,280 +Literals formula_to_literal(39,1157 +Literals formula_to_literals(59,1553 +Topform formula_to_clause(91,2367 +Plist formula_to_clauses(117,2962 +Plist clausify_formula(147,3746 +Term vars_to_names(170,4123 +Formula literal_to_formula(207,4852 +Formula clause_to_formula(231,5263 + +../ladr/clist.c,1622 +#define PTRS_CLIST_POS 27,841 +static unsigned Clist_pos_gets,28,895 +static unsigned Clist_pos_gets, Clist_pos_frees;28,895 +#define PTRS_CLIST 30,945 +static unsigned Clist_gets,31,991 +static unsigned Clist_gets, Clist_frees;31,991 +Clist_pos get_clist_pos(40,1109 +void free_clist_pos(54,1308 +Clist get_clist(67,1488 +void free_clist(81,1659 +void fprint_clist_mem(100,2031 +void p_clist_mem(132,2871 +Clist clist_init(155,3359 +void name_clist(178,3714 +void clist_free(201,4068 +void clist_append(223,4378 +void clist_prepend(255,4847 +void clist_insert_before(287,5333 +void clist_insert_after(319,5861 +void clist_remove(353,6518 +void clist_remove_all_clauses(397,7384 +int clist_remove_all(415,7735 +int clist_member(436,8061 +void fprint_clist(461,8549 +void p_clist(486,8968 +void clist_zap(504,9279 +void clist_check(532,9736 +void clist_append_all(570,10469 +BOOL clist_empty(589,10852 +int clist_length(604,11025 +int max_wt_in_clist(620,11248 +BOOL horn_clist(641,11587 +BOOL unit_clist(661,11901 +BOOL equality_in_clist(681,12244 +BOOL neg_nonunit_in_clist(701,12592 +Plist clauses_in_clist(722,13005 +void clist_swap(746,13489 +void clist_move_clauses(772,14011 +Plist move_clist_to_plist(791,14285 +Plist copy_clist_to_plist_shallow(814,14637 +Clist plist_to_clist(833,14955 +void clist_reverse(854,15260 +Clist_pos pos_in_clist(879,15637 +void clist_append_plist(896,15894 +Plist prepend_clist_to_plist(914,16159 +int clist_number_of_weight(936,16490 +Ordertype compare_clause_ids(958,16827 +void sort_clist_by_id(978,17126 +Plist neg_clauses_in_clist(1008,17641 +void fprint_clause_clist(1031,18092 + +../ladr/clock.c,937 +struct clock clock23,812 +static BOOL Clocks_enabled 30,1081 +static unsigned Clock_starts 31,1146 +static unsigned Wall_start;33,1203 +#define CPU_TIME(CPU_TIME42,1527 +#define CPU_TIME(CPU_TIME45,1674 +#define PTRS_CLOCK 52,1761 +static unsigned Clock_gets,53,1807 +static unsigned Clock_gets, Clock_frees;53,1807 +Clock get_clock(62,1917 +void free_clock(79,2115 +Clock clock_init(107,2663 +void clock_start(127,2968 +void clock_stop(151,3396 +unsigned clock_milliseconds(179,3912 +double clock_seconds(207,4372 +BOOL clock_running(234,4808 +void clock_reset(251,5106 +void fprint_clock(270,5325 +char * get_date(287,5644 +unsigned user_time(305,5933 +double user_seconds(329,6331 +unsigned system_time(356,6877 +double system_seconds(383,7425 +unsigned absolute_wallclock(405,7739 +void init_wallclock(422,8004 +unsigned wallclock(439,8293 +void disable_clocks(454,8474 +void enable_clocks(469,8646 +BOOL clocks_enabled(484,8816 + +../ladr/cnf.c,1177 +static jmp_buf Jump_env;41,1433 +static unsigned Fid_call_limit 43,1491 +static unsigned Fid_calls 44,1534 +Formula share_formula(53,1632 +Formula consolidate_formula(90,2386 +BOOL formula_ident_share(115,2931 +Formula formula_copy_share(152,3804 +BOOL complementary_share(180,4399 +BOOL contains_complements_share(197,4738 +BOOL prop_member_share(216,5099 +BOOL prop_subset_share(232,5423 +BOOL prop_subsume_share(250,5741 +Formula remove_subsumed_share(274,6226 +Formula bbt(316,7052 +Formula balanced_binary(338,7474 +Formula disjoin_flatten_simplify(360,7885 +Formula simplify_and_share(407,9049 +Formula distribute_top(436,9582 +Formula distribute(473,10375 +Formula cnf(502,10907 +Formula dnf(535,11490 +Formula skolem(547,11617 +Formula skolemize(621,13568 +Ilist unique_qvars(634,13719 +Formula unique_quantified_vars(679,14878 +void mark_free_vars_formula(697,15195 +Formula remove_uni_quant(717,15650 +Formula remove_universal_quantifiers(751,16407 +Formula clausify_prepare(781,17249 +Formula ms_free_vars(811,17860 +Formula miniscope(871,19356 +typedef void (*sighandler_t)sighandler_t932,20765 +Formula miniscope_formula(938,20835 +int cnf_max_clauses(990,22135 + +../ladr/complex.c,399 +#define IMAX(IMAX24,936 +double complexity1(51,1570 +double complexity2(111,2721 +double complexity3(152,3498 +Term complex4_devar(185,4140 +Term complex4_revar(207,4566 +void complex4_compare(229,4954 +BOOL complex4_p2(249,5423 +void complex4_p1(271,5813 +double complex4(302,6749 +void term_to_ints(335,7465 +double term_complexity(358,7801 +double clause_complexity(390,8370 +int main(401,8659 + +../ladr/compress.c,192 +Term uncompress_term(33,910 +void compress_term_recurse(55,1319 +char *compress_term(78,1696 +void compress_clause(103,2153 +void uncompress_clause(132,2862 +void uncompress_clauses(162,3508 + +../ladr/definitions.c,379 +BOOL is_definition(37,940 +Term subst_terms(78,1936 +void subst_free_vars(112,2782 +Formula subst_atomic_formula(135,3358 +Formula strip_quantifiers(174,4541 +BOOL definition_applies(188,4735 +Formula expand_with_definition(210,5158 +Topform first_definition(236,5869 +void process_definitions(260,6261 +void expand_with_definitions(303,7215 +void separate_definitions(344,8150 + +../ladr/demod.c,397 +static int Demod_attempts 26,866 +static int Demod_rewrites 27,897 +int demodulator_type(40,1100 +void idx_demodulator(90,2289 +int demod_attempts(117,2927 +int demod_rewrites(133,3167 +Term demod(147,3324 +Term contract_bt(207,4875 +Term demod_bt(242,5761 +Term demodulate(288,6961 +Term demod1_recurse(312,7536 +void demod1(372,8902 +Term part_recurse(403,9616 +void particular_demod(468,11105 + +../ladr/di_tree.c,869 +static int Nonunit_fsub_tests;23,814 +static int Nonunit_bsub_tests;24,845 +static unsigned Sub_calls 26,877 +static unsigned Sub_calls_overflows 27,908 +#define BUMP_SUB_CALLS 28,949 +int nonunit_fsub_tests(40,1133 +int nonunit_bsub_tests(55,1324 +#define PTRS_DI_TREE 64,1442 +static unsigned Di_tree_gets,65,1492 +static unsigned Di_tree_gets, Di_tree_frees;65,1492 +Di_tree get_di_tree(77,1637 +void free_di_tree(94,1849 +void fprint_di_tree_mem(113,2235 +void p_di_tree_mem(139,2855 +Di_tree init_di_tree(160,3152 +void di_tree_insert(175,3322 +BOOL di_tree_delete(215,4094 +void zap_di_tree(256,4984 +void p_di_tree(281,5358 +BOOL subsume_di_literals(311,5899 +BOOL subsumes_di(343,6538 +Topform di_tree_forward(359,6817 +Topform forward_feature_subsume(395,7566 +void di_tree_back(412,7903 +Plist back_feature_subsume(448,8685 +unsigned mega_sub_calls(469,9075 + +../ladr/dioph.c,641 +int gcd(28,860 +int lcm(44,1095 +int less_vec(57,1316 +int var_check_1(79,1794 +int var_check_2(105,2379 +int add_solution(131,2924 +int a_in_bounds(158,3623 +int b_in_bounds(199,4664 +int dio(242,5899 +#define ADD_TO_SUM(ADD_TO_SUM359,8409 +#define SUBTRACT_FROM_SUM(SUBTRACT_FROM_SUM362,8507 +int next_combo_a(391,9547 +int next_combo_b(451,10916 +#define DOWN 514,12188 +#define OVER 515,12206 +#define BACKUP 516,12224 +#define SUCCESS 517,12242 +#define FAILURE 518,12260 +int next_combo_c(527,12463 +int superset_degree(615,14638 +int next_combo_ss(661,16079 +void p_ac_basis(722,17305 +int all_combos(745,17807 +int main(790,18715 + +../ladr/discrim.c,598 +#define PTRS_DISCRIM 27,843 +static unsigned Discrim_gets,28,893 +static unsigned Discrim_gets, Discrim_frees;28,893 +#define PTRS_DISCRIM_POS 30,939 +static unsigned Discrim_pos_gets,31,997 +static unsigned Discrim_pos_gets, Discrim_pos_frees;31,997 +Discrim get_discrim(43,1150 +void free_discrim(60,1362 +Discrim_pos get_discrim_pos(77,1605 +void free_discrim_pos(94,1867 +void fprint_discrim_mem(113,2273 +void p_discrim_mem(145,3149 +Discrim discrim_init(166,3480 +void discrim_dealloc(182,3717 +void zap_discrim_tree(198,3950 +void destroy_discrim_tree(235,4636 +BOOL discrim_empty(252,4937 + +../ladr/discrimb.c,913 +typedef struct flat2 * Flat2;Flat227,844 +struct flat2 flat229,875 +#define GO 38,1079 +#define BACKTRACK 39,1099 +#define SUCCESS 40,1119 +#define FAILURE 41,1139 +#define PTRS_FLAT2 47,1189 +static unsigned Flat2_gets,48,1235 +static unsigned Flat2_gets, Flat2_frees;48,1235 +Flat2 get_flat2(57,1345 +void free_flat2(71,1516 +void fprint_discrimb_mem(90,1894 +void p_discrimb_mem(116,2504 +void print_discrim_bind_tree(132,2724 +void fprint_discrim_bind_index(176,3623 +void p_discrim_bind_index(192,3913 +Discrim discrim_bind_insert_rec(207,4231 +void discrim_bind_insert(279,5800 +Discrim discrim_bind_end(313,6725 +void discrim_bind_delete(364,7795 +void discrim_bind_update(447,9650 +Flat2 check_flat2(462,9927 +void p_flat2(489,10403 +Plist discrim_bind_retrieve_leaf(512,10803 +void *discrim_bind_retrieve_first(681,14446 +void *discrim_bind_retrieve_next(721,15400 +void discrim_bind_cancel(758,16255 + +../ladr/discrimw.c,1022 +typedef struct flat * Flat;Flat23,815 +struct flat flat25,844 +#define GO 38,1324 +#define BACKTRACK 39,1344 +#define SUCCESS 40,1364 +#define FAILURE 41,1384 +#define PTRS_FLAT 47,1434 +static unsigned Flat_gets,48,1478 +static unsigned Flat_gets, Flat_frees;48,1478 +Flat get_flat(57,1584 +void free_flat(85,1982 +void fprint_discrimw_mem(104,2355 +void p_discrimw_mem(130,2958 +Flat check_flat(146,3145 +void p_flat(173,3612 +void flip_flat(193,3918 +int num_ac_args(230,4647 +int num_ac_nv_args(246,4937 +void print_discrim_wild_tree(262,5259 +void fprint_discrim_wild_index(313,6394 +void p_discrim_wild_index(329,6685 +Discrim discrim_wild_insert_ac(341,6876 +Discrim discrim_wild_insert_rec(390,7938 +void discrim_wild_insert(459,9393 +Discrim discrim_wild_end(493,10311 +void discrim_wild_delete(568,11780 +void discrim_wild_update(650,13625 +Plist discrim_wild_retrieve_leaf(665,13937 +void *discrim_wild_retrieve_first(895,19451 +void *discrim_wild_retrieve_next(932,20234 +void discrim_wild_cancel(968,20980 + +../ladr/dollar.c,1127 +struct rule rule26,963 + SUM_OP=35,1067 + SUM_OP=1, PROD_OP,35,1067 + SUM_OP=1, PROD_OP, DIV_OP,35,1067 + SUM_OP=1, PROD_OP, DIV_OP, MOD_OP,35,1067 + SUM_OP=1, PROD_OP, DIV_OP, MOD_OP, MIN_OP,35,1067 + SUM_OP=1, PROD_OP, DIV_OP, MOD_OP, MIN_OP, MAX_OP,35,1067 + SUM_OP=1, PROD_OP, DIV_OP, MOD_OP, MIN_OP, MAX_OP, ABS_OP,35,1067 + NEG_OP,36,1128 + LT_OP,37,1138 + LT_OP, LE_OP,37,1138 + LT_OP, LE_OP, GT_OP,37,1138 + LT_OP, LE_OP, GT_OP, GE_OP,37,1138 + LLT_OP,38,1201 + LLT_OP, LLE_OP,38,1201 + LLT_OP, LLE_OP, LGT_OP,38,1201 + LLT_OP, LLE_OP, LGT_OP, LGE_OP,38,1201 + AND_OP,39,1261 + AND_OP, OR_OP,39,1261 + AND2_OP,40,1278 + AND2_OP, OR2_OP,40,1278 + IF_OP,41,1297 + ID_OP,42,1306 + ID_OP, NID_OP,42,1306 + VAR_OP,43,1381 + VAR_OP, CONST_OP,43,1381 + VAR_OP, CONST_OP, GROUND_OP}43,1381 +static int Symbols_size;45,1414 +static int *Op_codes;46,1439 +static struct rule **Rules;47,1461 +static int Local_evals;48,1489 +void init_dollar_eval(64,1639 +BOOL evaluable_predicate(167,4724 +Term dollar_eval(189,5046 +Term rewrite_top(364,8968 +Term rewrite(419,10202 +void rewrite_with_eval(510,11971 + +../ladr/fastparse.c,354 +static int Arity[23,816 +static int Symnum[24,883 +static int Pos;26,951 +#define MAX_LINE 28,1003 +void fast_set_symbol(48,1442 +void fast_set_defaults(79,2054 +Term fast_parse(105,2556 +Term fast_read_term(169,4110 +void fast_fwrite_term(201,4733 +void fast_fwrite_term_nl(245,5761 +Topform fast_read_clause(271,6328 +void fast_fwrite_clause(305,7065 + +../ladr/fatal.c,146 +static int Fatal_exit_code 23,812 +void bell(36,971 +int get_fatal_exit_code(53,1223 +void set_fatal_exit_code(70,1517 +void fatal_error(88,1880 + +../ladr/features.c,384 +static Ilist Feature_symbols;23,815 +static int Work_size;30,1078 +static int *Pos_occurrences;31,1139 +static int *Neg_occurrences;32,1168 +static int *Pos_maxdepth;33,1197 +static int *Neg_maxdepth;34,1223 +void init_features(46,1343 +void fill_in_arrays(66,1852 +Ilist features(114,2905 +int feature_length(161,3850 +BOOL features_less_or_equal(185,4281 +void p_features(204,4544 + +../ladr/flatdemod.c,528 +static int Fdemod_attempts 23,816 +static int Fdemod_rewrites 24,848 +Flatterm fapply_demod(45,1284 +enum { GO,75,1854 +enum { GO, BACKTRACK 75,1854 +void maybe_unbind(85,1964 +#define MAYBE_UNBIND(MAYBE_UNBIND94,2152 +Plist discrim_flat_retrieve_leaf(100,2309 +void *discrim_flat_retrieve_first(187,3981 +void *discrim_flat_retrieve_next(217,4536 +void discrim_flat_cancel(250,5155 +Flatterm fdemod(272,5561 +Term fdemodulate(387,8548 +int fdemod_attempts(426,9492 +int fdemod_rewrites(442,9721 +void fdemod_clause(462,10083 + +../ladr/flatterm.c,646 +#define PTRS_FLATTERM 27,844 +static unsigned Flatterm_gets,28,896 +static unsigned Flatterm_gets, Flatterm_frees;28,896 +Flatterm get_flatterm(40,1045 +void free_flatterm(63,1450 +void fprint_flatterm_mem(82,1843 +void p_flatterm_mem(108,2474 +BOOL flatterm_ident(127,2691 +void zap_flatterm(146,3031 +Flatterm term_to_flatterm(166,3302 +Term flatterm_to_term(204,3921 +Flatterm copy_flatterm(230,4367 +void print_flatterm(264,4906 +int flatterm_symbol_count(300,5563 +void p_flatterm(326,5941 +BOOL flat_occurs_in(342,6123 +I2list flat_multiset_vars(361,6434 +BOOL flat_variables_multisubset(381,6778 +int flatterm_count_without_vars(401,7167 + +../ladr/formula.c,2323 +#define PTRS_FORMULA 27,843 +static unsigned Formula_gets,28,893 +static unsigned Formula_gets, Formula_frees;28,893 +static unsigned Arg_mem;30,939 +Formula get_formula(39,1081 +void free_formula(59,1367 +void fprint_formula_mem(82,1891 +void p_formula_mem(111,2630 +unsigned formula_megs(131,2917 +Formula formula_get(151,3208 +void zap_formula(170,3576 +BOOL logic_term(200,4042 +void gather_symbols_in_term(220,4455 +void gather_symbols_in_formula_term(248,5073 +void gather_symbols_in_formula(277,5701 +void gather_symbols_in_formulas(305,6386 +Ilist function_symbols_in_formula(322,6699 +Ilist relation_symbols_in_formula(344,7080 +BOOL relation_symbol_in_formula(366,7460 +Formula term_to_formula(386,7870 +Term formula_to_term(459,9600 +void fprint_formula(533,11467 +void p_formula(602,13310 +unsigned hash_formula(621,13611 +BOOL formula_ident(652,14307 +Formula formula_copy(682,14976 +BOOL dual_type(708,15395 +Formula dual(730,15755 +Formula and(750,16001 +Formula or(768,16221 +Formula imp(786,16439 +Formula impby(804,16662 +Formula not(819,16862 +Formula negate(836,17057 +BOOL quant_form(851,17241 +Formula flatten_top(866,17466 +Formula formula_flatten(922,18562 +Formula nnf2(949,19247 +Formula nnf(1069,22166 +Formula make_conjunction(1085,22381 +Formula make_disjunction(1107,22721 +void formula_canon_eq(1130,23122 +int formula_size(1161,23679 +int greatest_qvar(1189,24231 +int greatest_symnum_in_formula(1222,24937 +void subst_free_var(1256,25698 +Formula elim_rebind(1277,26210 +Formula eliminate_rebinding(1332,27677 +Plist free_vars(1345,27850 +BOOL closed_formula(1374,28407 +Formula get_quant_form(1392,28686 +Formula uni_close(1407,28935 +Formula universal_closure(1430,29364 +BOOL free_var(1445,29616 +BOOL free_variable(1472,30064 +Formula formulas_to_conjunction(1495,30575 +Formula formulas_to_disjunction(1522,31168 +Plist copy_plist_of_formulas(1544,31530 +BOOL literal_formula(1567,31927 +BOOL clausal_formula(1587,32226 +void formula_set_vars_recurse(1608,32559 +void formula_set_variables(1639,33407 +BOOL positive_formula(1697,34792 +BOOL formula_contains_attributes(1726,35312 +BOOL subformula_contains_attributes(1752,35792 +Ilist constants_in_formula(1775,36170 +BOOL relation_in_formula(1792,36426 +void rename_all_bound_vars(1815,36815 +void rename_these_bound_vars(1843,37364 + +../ladr/fpa.c,2247 +static unsigned Fpa_id_count 23,810 +static unsigned Next_calls 25,845 +static unsigned Next_calls_overflows 26,877 +#define BUMP_NEXT_CALLS 27,919 +typedef struct fpa_trie * Fpa_trie;Fpa_trie29,1005 +struct fpa_trie fpa_trie31,1042 +struct fpa_index fpa_index40,1180 +struct fpa_state fpa_state46,1261 +struct path path61,1661 +enum { LEAF,66,1708 +enum { LEAF, UNION,66,1708 +enum { LEAF, UNION, INTERSECT 66,1708 +#define PTRS_FPA_TRIE 77,1963 +static unsigned Fpa_trie_gets,78,2015 +static unsigned Fpa_trie_gets, Fpa_trie_frees;78,2015 +#define PTRS_FPA_STATE 80,2063 +static unsigned Fpa_state_gets,81,2117 +static unsigned Fpa_state_gets, Fpa_state_frees;81,2117 +#define PTRS_FPA_INDEX 83,2167 +static unsigned Fpa_index_gets,84,2221 +static unsigned Fpa_index_gets, Fpa_index_frees;84,2221 +Fpa_trie get_fpa_trie(93,2345 +void free_fpa_trie(108,2554 +Fpa_state get_fpa_state(121,2737 +void free_fpa_state(135,2936 +Fpa_index get_fpa_index(148,3124 +void free_fpa_index(163,3340 +void fprint_fpa_mem(182,3728 +void p_fpa_mem(220,4823 +void fprint_path(240,5096 +void p_path(271,5602 +void fprint_fpa_trie(284,5785 +void fprint_fpa_index(326,6666 +void p_fpa_index(345,7117 +Fpa_trie fpa_trie_member_insert(360,7486 +Fpa_trie fpa_trie_member(400,8533 +void fpa_trie_possible_delete(430,9371 +void path_insert(457,9995 +void path_delete(479,10475 +Ilist path_push(506,11060 +void path_restore(529,11490 +void fpa_paths(548,11912 +Fpa_index fpa_init_index(591,12904 +void fpa_update(616,13461 +Fpa_state query_leaf_full(645,14164 +Fpa_state query_leaf(663,14497 +Fpa_state query_intersect(690,14941 +Fpa_state query_union(707,15219 +Fpa_state query_special(729,15561 +void zap_fpa_state(779,16950 +Fpa_state union_commuted(798,17226 +BOOL var_in_context(846,18193 +BOOL all_args_vars_in_context(859,18379 +Fpa_state build_query(878,18691 +void fprint_fpa_state(961,21085 +void p_fpa_state(1007,22033 +void p_fpa_query(1023,22283 +Term next_term(1063,23565 +Term fpa_next_answer(1180,26140 +Term fpa_first_answer(1206,26777 +void fpa_cancel(1229,27278 +void zap_fpa_trie(1241,27415 +void zap_fpa_index(1273,27873 +BOOL fpa_empty(1290,28131 +void fpa_density(1302,28304 +void p_fpa_density(1325,28682 +unsigned mega_next_calls(1340,28864 + +../ladr/fpalist.c,985 +#define F_INITIAL_SIZE 48,1970 +#define F_MAX_SIZE 49,2050 +#define PTRS_FPA_CHUNK 55,2135 +static unsigned Fpa_chunk_gets,56,2189 +static unsigned Fpa_chunk_gets, Fpa_chunk_frees;56,2189 +#define PTRS_FPA_LIST 58,2239 +static unsigned Fpa_list_gets,59,2291 +static unsigned Fpa_list_gets, Fpa_list_frees;59,2291 +static unsigned Chunk_mem;61,2339 +Fpa_chunk get_fpa_chunk(70,2493 +void free_fpa_chunk(87,2748 +Fpa_list get_fpa_list(105,3012 +void free_fpa_list(120,3233 +void fprint_fpalist_mem(139,3624 +void p_fpalist_mem(173,4613 +#define FLAST(FLAST184,4799 +#define FFIRST(FFIRST185,4838 +Fpa_chunk double_chunksize(194,4953 +Fpa_chunk flist_insert(232,5850 +void fpalist_insert(314,7782 +Fpa_chunk consolidate(344,8542 +Fpa_chunk flist_delete(367,8977 +void fpalist_delete(413,9894 +struct fposition first_fpos(433,10232 +struct fposition next_fpos(448,10440 +void zap_fpa_chunks(474,10917 +void zap_fpalist(492,11143 +BOOL fpalist_empty(508,11338 +void p_fpa_list(523,11519 + +../ladr/glist.c,3091 +#define PTRS_ILIST 25,804 +static unsigned Ilist_gets,26,850 +static unsigned Ilist_gets, Ilist_frees;26,850 +#define PTRS_PLIST 28,892 +static unsigned Plist_gets,29,938 +static unsigned Plist_gets, Plist_frees;29,938 +#define PTRS_I2LIST 31,980 +static unsigned I2list_gets,32,1028 +static unsigned I2list_gets, I2list_frees;32,1028 +#define PTRS_I3LIST 34,1072 +static unsigned I3list_gets,35,1120 +static unsigned I3list_gets, I3list_frees;35,1120 +Ilist get_ilist(47,1259 +void free_ilist(65,1474 +Plist get_plist(81,1661 +void free_plist(99,1876 +I2list get_i2list(115,2065 +void free_i2list(133,2287 +I3list get_i3list(149,2481 +void free_i3list(167,2703 +void fprint_glist_mem(186,3080 +void p_glist_mem(224,4113 +Plist plist_cat(251,4747 +Plist plist_cat2(282,5266 +Plist plist_pop(299,5589 +int plist_count(318,5830 +Plist rev_app_plist(332,6009 +Plist reverse_plist(361,6506 +Plist copy_plist(377,6752 +void zap_plist(408,7226 +Plist plist_append(432,7563 +Plist plist_prepend(458,7987 +BOOL plist_member(477,8269 +Plist plist_subtract(500,8630 +BOOL plist_subset(523,8978 +Plist plist_remove(544,9317 +Plist plist_remove_string(572,9760 +Plist sort_plist(599,10177 +Plist plist_remove_last(624,10653 +int position_of_string_in_plist(649,11055 +BOOL string_member_plist(674,11454 +int longest_string_in_plist(690,11714 +void *ith_in_plist(711,12022 +void *plist_last(731,12298 +Ilist ilist_cat(759,12990 +Ilist ilist_cat2(788,13481 +Ilist ilist_pop(810,13878 +int ilist_count(829,14119 +Ilist rev_app_ilist(843,14298 +Ilist reverse_ilist(872,14795 +Ilist copy_ilist(888,15041 +void zap_ilist(918,15461 +Ilist ilist_append(942,15799 +Ilist ilist_prepend(968,16222 +Ilist ilist_last(986,16442 +BOOL ilist_member(1009,16859 +Ilist ilist_subtract(1032,17218 +Ilist ilist_removeall(1058,17629 +Ilist ilist_intersect(1086,18078 +Ilist ilist_union(1114,18550 +Ilist ilist_set(1137,19085 +Ilist ilist_rem_dups(1163,19488 +BOOL ilist_is_set(1190,19851 +BOOL ilist_subset(1210,20128 +void fprint_ilist(1232,20497 +void p_ilist(1255,20899 +Ilist ilist_copy(1272,21092 +Ilist ilist_remove_last(1294,21386 +int ilist_occurrences(1319,21769 +Ilist ilist_insert_up(1337,22034 +int position_in_ilist(1362,22431 +void zap_i2list(1392,23069 +I2list i2list_append(1416,23415 +I2list i2list_prepend(1443,23879 +I2list i2list_removeall(1465,24190 +I2list i2list_member(1490,24565 +void p_i2list(1512,24930 +int i2list_count(1534,25272 +BOOL i3list_member(1556,25786 +I3list i3list_append(1578,26196 +I3list i3list_prepend(1606,26684 +void zap_i3list(1627,26995 +I3list rev_app_i3list(1646,27243 +I3list reverse_i3list(1675,27751 +I3list copy_i3list(1691,28005 +int i3list_count(1723,28469 +I2list alist_insert(1750,29242 +int assoc(1766,29456 +I3list alist2_insert(1793,30040 +int assoc2a(1809,30265 +int assoc2b(1831,30591 +I3list alist2_remove(1852,30904 +BOOL i2list_multimember(1889,31720 +BOOL i2list_multisubset(1909,32029 +I2list multiset_add_n(1930,32385 +I2list multiset_add(1955,32761 +I2list multiset_union(1973,33095 +Ilist multiset_to_set(1992,33369 +int multiset_occurrences(2014,33674 + +../ladr/hash.c,644 +struct hashtab hashtab23,811 +struct hashnode hashnode28,868 +#define PTRS_HASHTAB 37,952 +static unsigned Hashtab_gets,38,1002 +static unsigned Hashtab_gets, Hashtab_frees;38,1002 +#define PTRS_HASHNODE 40,1048 +static unsigned Hashnode_gets,41,1100 +static unsigned Hashnode_gets, Hashnode_frees;41,1100 +Hashtab get_hashtab(50,1220 +void free_hashtab(64,1405 +Hashnode get_hashnode(77,1581 +void free_hashnode(91,1773 +void fprint_hash_mem(110,2158 +void p_hash_mem(142,3001 +Hashtab hash_init(161,3256 +void hash_insert(180,3502 +void *hash_lookup(199,3796 +void hash_delete(220,4134 +void hash_destroy(255,4798 +void hash_info(280,5152 + +../ladr/hints.c,647 +static Lindex Hints_idx 23,812 +static Clist Redundant_hints 24,876 +static Mindex Back_demod_idx;25,946 +static int Bsub_wt_attr;26,1026 +static BOOL Back_demod_hints;27,1051 +static BOOL Collect_labels;28,1081 +static int Hint_id_count 36,1258 +static int Active_hints_count 37,1288 +static int Redundant_hints_count 38,1323 +void init_hints(50,1452 +void done_with_hints(76,2040 +int redundant_hints(99,2474 +Topform find_equivalent_hint(111,2641 +Topform find_matching_hint(139,3373 +void index_hint(168,4042 +void unindex_hint(208,5136 +void adjust_weight_with_hints(232,5571 +void keep_hint_matcher(300,7373 +void back_demod_hints(316,7586 + +../ladr/ibuffer.c,317 +Ibuffer ibuf_init(39,1002 +void ibuf_free(60,1356 +void ibuf_write(77,1562 +void ibuf_write_block(106,2183 +void ibuf_rewind(124,2447 +int ibuf_read(141,2725 +int ibuf_xread(165,3175 +int ibuf_length(185,3499 +int *ibuf_buffer(200,3675 +#define ISIZE 211,3811 +Ibuffer fd_read_to_ibuf(217,3864 +void p_ibuf(254,4562 + +../ladr/int_code.c,374 +void put_ilist_to_ibuf(30,885 +Ilist get_ilist_from_ibuf(45,1158 +void put_i3list_to_ibuf(63,1473 +I3list get_i3list_from_ibuf(81,1814 +void put_term_to_ibuf(103,2226 +Term get_term_from_ibuf(123,2563 +void put_just_to_ibuf(150,3118 +Just get_just_from_ibuf(208,4462 +void put_clause_to_ibuf(277,6069 +Topform get_clause_from_ibuf(312,6775 +void check_ibuf_clause(348,7493 + +../ladr/interp.c,2821 +struct interp interp28,878 +#define ISWAP(ISWAP50,1726 +#define I2(I254,1828 +#define I3(I355,1868 +#define UNDEFINED 57,1927 +#define FUNCTION 58,1947 +#define RELATION 59,1967 +#define MAX_VARS_EVAL 61,1988 +static long unsigned Iso_checks 65,2033 +static long unsigned Iso_perms 66,2070 +#define PTRS_INTERP 72,2136 +static unsigned Interp_gets,73,2184 +static unsigned Interp_gets, Interp_frees;73,2184 +Interp get_interp(82,2298 +void free_interp(96,2476 +void fprint_interp_mem(115,2855 +void p_interp_mem(141,3464 +int *trivial_permutation(157,3653 +int int_power(179,4009 +Interp compile_interp(219,4800 +void transpose_binary(355,8547 +void zap_interp(394,9407 +void fprint_interp_tex(436,10153 +void compute_args(535,12726 +void fprint_interp_xml(558,13122 +void fprint_interp_standard(669,16515 +void fprint_interp_standard2(727,17968 +static void portable_indent(785,19409 +void portable_recurse(800,19634 +void fprint_interp_portable(834,20417 +void p_interp(891,21744 +void fprint_interp_cooked(908,22019 +void fprint_interp_tabular(979,23652 +void fprint_interp_raw(1065,25522 +int eval_term_ground(1120,26821 +BOOL eval_literals_ground(1169,27986 +BOOL all_recurse(1195,28581 +BOOL eval_literals(1238,29798 +int all_recurse2(1263,30229 +int eval_literals_true_instances(1295,31009 +int eval_literals_false_instances(1322,31558 +int eval_fterm_ground(1340,32021 +BOOL eval_form(1390,33153 +BOOL eval_formula(1483,35753 +Term interp_remove_constants_recurse(1524,36471 +void interp_remove_constants(1552,37072 +Term interp_remove_others_recurse(1568,37362 +void interp_remove_others(1596,38002 +Interp copy_interp(1612,38304 +Interp permute_interp(1697,40420 +BOOL ident_interp_perm(1765,42087 +Interp normal_interp(1846,44462 +BOOL iso_interp_recurse(1890,45364 +BOOL isomorphic_interps(1931,46353 +int interp_size(1969,47049 +Term interp_comments(1985,47257 +int *interp_table(2001,47488 +long unsigned iso_checks(2022,47898 +long unsigned iso_perms(2038,48128 +BOOL evaluable_term(2053,48294 +BOOL evaluable_atom(2084,48896 +BOOL evaluable_literals(2115,49511 +BOOL evaluable_formula(2134,49818 +BOOL evaluable_topform(2157,50192 +void update_interp_with_constant(2175,50497 +BOOL eval_topform(2201,51060 +Ordertype compare_interp(2221,51416 +BOOL ident_interp(2254,52054 +Ordertype compare_ints(2260,52165 +void invert_perm(2271,52339 +void copy_perm(2279,52462 +Ordertype compare_permed_interps(2301,52814 +void canon_recurse(2376,54556 +Interp canon_interp(2426,55803 +void assign_discriminator_counts(2460,56579 +BOOL same_discriminator_counts(2484,57099 +void update_profile(2503,57518 +void create_profile(2538,58246 +void p_interp_profile(2573,59022 +Interp normal3_interp(2625,60257 +BOOL same_profiles(2695,61897 +long unsigned perms_required(2715,62230 +long unsigned factorial(2750,62758 + +../ladr/ioutil.c,1118 +void fwrite_formula(39,1187 +Topform read_clause(66,1781 +Topform parse_clause_from_string(89,2167 +BOOL end_of_list_clause(108,2509 +Clist read_clause_clist(139,3248 +Plist read_clause_list(168,3865 +void sb_write_clause_jmap(185,4223 +void sb_write_clause(245,5407 +void sb_xml_write_clause_jmap(262,5747 +void sb_tagged_write_clause_jmap(328,7779 +void fwrite_clause_jmap(372,8576 +void fwrite_clause(405,9332 +void f_clause(421,9601 +void fwrite_clause_clist(444,9974 +void fwrite_demod_clist(470,10547 +void fwrite_clause_list(510,11400 +void f_clauses(535,11865 +Formula read_formula(554,12238 +BOOL end_of_list_formula(576,12553 +Plist read_formula_list(605,13137 +void fwrite_formula_list(639,13751 +void zap_formula_list(665,14232 +BOOL end_of_list_term(687,14559 +BOOL end_of_commands_term(708,14905 +Plist read_term_list(735,15512 +void fwrite_term_list(769,16107 +Term term_reader(801,16807 +void term_writer(823,17271 +Topform clause_reader(847,17767 +void clause_writer(863,18187 +Topform term_to_topform2(882,18466 +Topform read_clause_or_formula(912,19033 +Plist read_clause_or_formula_list(934,19379 + +../ladr/ivy.c,790 +#define DICT_SIZE 23,810 +static char *Dict[27,895 +char *dict_lookup(40,1177 +void ivy_term_trans(57,1422 +void ivy_clause_trans(78,1779 +void sb_ivy_write_term(93,2012 +void sb_ivy_write_pair(118,2462 +void sb_ivy_write_pairs(136,2784 +void sb_ivy_write_position(155,3113 +void sb_ivy_write_lit(174,3445 +void sb_ivy_write_literals(192,3766 +void sb_ivy_write_just(217,4228 +void sb_ivy_write_clause_jmap(275,5687 +Topform instantiate_inference(299,6422 +Topform renumber_inference(316,6902 +Ilist ivy_lit_position(339,7358 +Ilist ivy_para_position(368,8198 +Plist paramod2_instances(396,8920 +Topform flip_inference(481,11512 +Plist resolve2_instances(524,12674 +Plist factor2_instances(621,15016 +Plist copy_proof_and_rename_symbols_for_ivy(682,16548 +Plist expand_proof_ivy(704,16948 + +../ladr/just.c,2701 +#define PTRS_JUST 27,840 +static unsigned Just_gets,28,884 +static unsigned Just_gets, Just_frees;28,884 +#define PTRS_PARAJUST 30,924 +static unsigned Parajust_gets,31,976 +static unsigned Parajust_gets, Parajust_frees;31,976 +#define PTRS_INSTANCEJUST 33,1024 +static unsigned Instancejust_gets,34,1084 +static unsigned Instancejust_gets, Instancejust_frees;34,1084 +#define PTRS_IVYJUST 36,1140 +static unsigned Ivyjust_gets,37,1190 +static unsigned Ivyjust_gets, Ivyjust_frees;37,1190 +Just get_just(49,1329 +void free_just(63,1493 +Parajust get_parajust(79,1681 +void free_parajust(93,1873 +Instancejust get_instancejust(109,2089 +void free_instancejust(123,2309 +Ivyjust get_ivyjust(136,2508 +void free_ivyjust(150,2692 +void fprint_just_mem(169,3072 +void p_just_mem(213,4385 +Just ivy_just(232,4584 +Just input_just(260,5122 +Just goal_just(279,5399 +Just deny_just(298,5672 +Just clausify_just(318,5979 +Just expand_def_just(338,6306 +Just copy_just(358,6686 +Just propositional_just(378,7011 +Just new_symbol_just(398,7376 +Just back_demod_just(418,7719 +Just back_unit_deletion_just(438,8078 +Just binary_res_just(460,8541 +Just binary_res_just_by_id(484,9082 +Just factor_just(508,9609 +Just xxres_just(528,10030 +Just resolve_just(549,10454 +Just demod_just(568,10749 +Just para_just(588,11095 +Just instance_just(616,11650 +Just para_just_rev_copy(640,12131 +Just unit_del_just(660,12557 +Just flip_just(680,12966 +Just xx_just(700,13286 +Just merge_just(721,13641 +Just eval_just(741,13959 +Just append_just(760,14220 +Just copy_justification(781,14502 +char *jstring(859,16592 +int jstring_to_jtype(907,18115 +char itoc(974,19897 +int ctoi(993,20130 +int jmap1(1015,20486 +char *jmap2(1039,20998 +void sb_append_id(1065,21403 +void sb_write_res_just(1081,21733 +void sb_write_position(1120,22565 +void sb_write_ids(1142,22947 +void sb_write_just(1164,23346 +void sb_xml_write_just(1324,27317 +void p_just(1371,28377 +void zap_parajust(1387,28617 +void zap_instancejust(1401,28813 +void zap_ivyjust(1414,29000 +void zap_just(1433,29300 +Ilist get_parents(1491,30600 +Topform first_negative_parent(1586,33386 +Plist get_clanc(1607,33826 +Plist get_clause_ancestors(1643,34667 +int proof_length(1659,34894 +int map_id(1671,35037 +void map_just(1688,35301 +int just_count(1780,37903 +void mark_parents_as_used(1797,38119 +I2list cl_level(1815,38451 +int clause_level(1849,39245 +int lit_string_to_int(1864,39488 +Ilist args_to_ilist(1882,39739 +Just term_to_just(1914,40333 +BOOL primary_just_type(2078,43902 +BOOL has_input_just(2094,44174 +BOOL has_copy_just(2110,44409 +BOOL has_copy_flip_just(2126,44670 +void sb_tagged_write_res_just(2148,45325 +void sb_tagged_write_just(2183,46015 + +../ladr/lindex.c,409 +#define PTRS_LINDEX 27,842 +static unsigned Lindex_gets,28,890 +static unsigned Lindex_gets, Lindex_frees;28,890 +Lindex get_lindex(37,1004 +void free_lindex(51,1182 +void fprint_lindex_mem(70,1561 +void p_lindex_mem(96,2170 +Lindex lindex_init(126,2904 +void lindex_destroy(149,3447 +void lindex_update(167,3737 +void lindex_update_first(189,4181 +BOOL lindex_empty(212,4636 +BOOL lindex_backtrack(229,4949 + +../ladr/listterm.c,413 +#define CONS_SYM 23,815 +#define NIL_SYM 24,841 +Term get_nil_term(37,998 +Term listterm_cons(54,1249 +BOOL cons_term(74,1584 +BOOL nil_term(91,1856 +BOOL proper_listterm(109,2165 +Term listterm_append(137,2839 +int listterm_length(158,3208 +Term listterm_i(179,3547 +BOOL listterm_member(200,3896 +Plist listterm_to_tlist(224,4321 +void listterm_zap(249,4709 +Term rev2(266,4914 +Term listterm_reverse(286,5279 + +../ladr/literals.c,1875 +#define PTRS_LITERALS 27,844 +static unsigned Literals_gets,28,896 +static unsigned Literals_gets, Literals_frees;28,896 +Literals get_literals(40,1045 +void free_literals(57,1264 +void fprint_literals_mem(76,1655 +void p_literals_mem(102,2284 +void zap_literal(122,2527 +void zap_literals(139,2754 +Literals new_literal(159,3063 +Literals copy_literal(177,3308 +Literals append_literal(193,3572 +Literals term_to_literals(213,3864 +Term literal_to_term(248,4584 +Term literals_to_term(270,4892 +Term lits_to_term(297,5513 +void free_lits_to_term(327,6046 +int positive_literals(349,6449 +int negative_literals(370,6832 +BOOL positive_clause(391,7217 +BOOL any_clause(407,7485 +BOOL negative_clause(423,7719 +BOOL mixed_clause(440,8008 +int number_of_literals(457,8298 +BOOL unit_clause(476,8604 +BOOL horn_clause(492,8861 +BOOL definite_clause(508,9129 +int greatest_variable_in_clause(525,9443 +Plist vars_in_clause(547,9888 +Ilist varnums_in_clause(566,10233 +int number_of_variables(590,10686 +BOOL ground_clause(608,10947 +Literals copy_literals(626,11272 +Literals copy_literals_with_flags(652,11785 +Literals copy_literals_with_flag(678,12334 +int literal_number(704,12938 +int atom_number(729,13444 +Literals ith_literal(753,13853 +BOOL true_clause(775,14233 +BOOL complementary_scan(792,14506 +BOOL tautology(815,15004 +int symbol_occurrences_in_clause(839,15441 +Literals remove_null_literals(859,15797 +Literals first_literal_of_sign(885,16191 +Ilist constants_in_clause(906,16590 +BOOL clause_ident(927,16968 +int clause_symbol_count(952,17478 +int clause_depth(972,17872 +BOOL pos_eq(995,18305 +BOOL neg_eq(1012,18588 +BOOL pos_eq_unit(1029,18899 +BOOL neg_eq_unit(1047,19191 +BOOL contains_pos_eq(1066,19539 +BOOL contains_eq(1089,19959 +BOOL only_eq(1111,20321 +int literals_depth(1133,20707 +Term term_at_position(1154,21010 +Ilist pos_predicates(1175,21354 + +../ladr/maximal.c,539 +int Maximal_flag 23,814 +int Maximal_signed_flag 24,886 +int Selected_flag 25,961 +void init_maximal(37,1118 +BOOL greater_literals(53,1434 +BOOL max_lit_test(83,2124 +BOOL max_signed_lit_test(110,2672 +void mark_maximal_literals(134,3148 +BOOL maximal_literal(164,3873 +BOOL maximal_signed_literal(184,4301 +int number_of_maximal_literals(203,4706 +void mark_selected_literal(224,5045 +void mark_selected_literals(239,5265 +BOOL selected_literal(270,5924 +BOOL exists_selected_literal(285,6138 +void copy_selected_literal_marks(304,6448 + +../ladr/memory.c,816 +#define MALLOC_MEGS 21,776 +#define DEFAULT_MAX_MEGS 22,847 +#define MAX_MEM_LISTS 23,912 +static void ** M[25,985 +static BOOL Max_megs_check 27,1019 +static int Max_megs 28,1054 +static int Malloc_calls 31,1206 +static unsigned Bytes_palloced 33,1280 +static void *Block 35,1317 +static void *Block_pos 36,1397 +static unsigned Mem_calls 38,1464 +static unsigned Mem_calls_overflows 39,1495 +#define BUMP_MEM_CALLS 41,1537 +void *palloc(50,1728 +void *get_cmem(96,2788 +void *get_mem(134,3421 +void free_mem(166,4013 +int mlist_length(190,4401 +void memory_report(207,4598 +int megs_malloced(233,5277 +void set_max_megs(251,5617 +void set_max_megs_proc(268,5900 +int bytes_palloced(285,6189 +void *tp_alloc(302,6468 +unsigned mega_mem_calls(321,6786 +void disable_max_megs(338,7026 +void enable_max_megs(353,7204 + +../ladr/mindex.c,948 +struct mindex_pos mindex_pos23,813 +#define PTRS_MINDEX 53,1371 +static unsigned Mindex_gets,54,1419 +static unsigned Mindex_gets, Mindex_frees;54,1419 +#define PTRS_MINDEX_POS 56,1463 +static unsigned Mindex_pos_gets,57,1519 +static unsigned Mindex_pos_gets, Mindex_pos_frees;57,1519 +Mindex get_mindex(66,1641 +void free_mindex(82,1862 +Mindex_pos get_mindex_pos(95,2037 +void free_mindex_pos(110,2265 +void fprint_mindex_mem(129,2664 +void p_mindex_mem(161,3522 +Mindex mindex_init(204,4833 +BOOL mindex_empty(234,5560 +void mindex_free(263,6056 +void mindex_destroy(295,6675 +void linear_insert(324,7230 +void linear_delete(343,7538 +void linear_update(375,8158 +void mindex_update(398,8628 +Term mindex_retrieve_first(465,10746 +Term next_candidate(510,11865 +Term retrieve_next_backtrack(565,13185 +Term mindex_retrieve_next(643,15321 +void mindex_retrieve_cancel(733,17311 +void fprint_linear_index(765,18162 +void fprint_mindex(787,18560 + +../ladr/multiset.c,98 +int num_occurrences(30,883 +Plist set_of_more_occurrences(48,1211 +BOOL greater_multiset(83,2083 + +../ladr/nonport.c,98 +char *username(42,1117 +char *hostname(64,1471 +int my_process_id(87,1826 +int get_bits(107,2093 + +../ladr/options.c,2570 +typedef enum { FLAGT,28,892 +typedef enum { FLAGT, PARMT,28,892 +typedef enum { FLAGT, PARMT, FLOATPARMT,28,892 +typedef enum { FLAGT, PARMT, FLOATPARMT, STRINGPARMT 28,892 +typedef enum { FLAGT, PARMT, FLOATPARMT, STRINGPARMT } Opttype;Opttype28,892 +typedef struct optdep * Optdep;Optdep29,956 +struct optdep optdep31,989 +struct flag flag42,1544 +struct parm parm49,1671 +struct floatparm floatparm57,1858 +struct stringparm stringparm65,2063 +static struct flag Flags[74,2414 +static struct parm Parms[75,2451 +static struct floatparm Floatparms[76,2488 +static struct stringparm Stringparms[77,2540 +static int Next_flag 79,2596 +static int Next_parm 80,2622 +static int Next_floatparm 81,2648 +static int Next_stringparm 82,2679 +static int Option_updates 84,2712 +static BOOL Ignore_dependencies 86,2774 +#define PTRS_OPTDEP 92,2845 +static unsigned Optdep_gets,93,2893 +static unsigned Optdep_gets, Optdep_frees;93,2893 +Optdep get_optdep(102,3007 +void free_optdep(117,3191 +void fprint_options_mem(137,3579 +void p_options_mem(163,4192 +void enable_option_dependencies(182,4418 +void disable_option_dependencies(197,4633 +BOOL option_dependencies_state(212,4847 +int init_flag(232,5286 +int init_parm(269,6140 +int init_floatparm(304,6932 +int init_stringparm(343,7903 +void fprint_options(380,8848 +void p_options(433,10186 +int flag(451,10449 +int parm(468,10715 +BOOL at_parm_limit(484,10918 +BOOL over_parm_limit(504,11245 +double floatparm(525,11646 +BOOL stringparm(542,11938 +char *stringparm1(559,12207 +void update_flag(576,12495 +void set_flag(654,14482 +void clear_flag(672,14825 +void assign_parm(691,15219 +void assign_floatparm(753,16903 +void assign_stringparm(788,18079 +int str_to_flag_id(827,19037 +int str_to_parm_id(848,19417 +int str_to_floatparm_id(869,19802 +int str_to_stringparm_id(890,20214 +char *flag_id_to_str(910,20562 +char *parm_id_to_str(928,20873 +char *floatparm_id_to_str(946,21199 +char *stringparm_id_to_str(964,21553 +Optdep append_dep(978,21803 +void flag_flag_dependency(1001,22217 +void flag_flag_dep_default(1024,22759 +void flag_parm_dependency(1047,23298 +void flag_floatparm_dependency(1070,23840 +void flag_parm_dep_default(1093,24394 +void flag_floatparm_dep_default(1116,24941 +void parm_flag_dependency(1139,25497 +void parm_parm_dependency(1160,25974 +void flag_stringparm_dependency(1183,26530 +void flag_stringparm_dep_default(1206,27104 +int option_updates(1227,27582 +int flag_default(1242,27751 +int parm_default(1257,27935 +int floatparm_default(1272,28124 +char *stringparm1_default(1287,28340 + +../ladr/order.c,116 +void merge_sort_recurse(49,1403 +void merge_sort(110,2752 +Ordertype compare_vecs(129,3112 +void copy_vec(151,3428 + +../ladr/paramod.c,839 +static BOOL Ordered_inference 23,814 +static BOOL Positive_inference 24,854 +static BOOL Para_from_vars 25,895 +static BOOL Para_into_vars 26,931 +static BOOL Para_from_small 27,968 +static BOOL Check_instances 28,1006 +static int Para_instance_prunes 30,1077 +static int Basic_prunes 31,1132 +void paramodulation_options(44,1291 +int para_instance_prunes(73,1977 +int basic_paramodulation_prunes(89,2248 +BOOL basic_check(101,2413 +Literals apply_lit_para(118,2656 +Term apply_substitute_para(134,2960 +Topform paramodulate(156,3402 +BOOL para_from_right(200,4715 +BOOL from_parent_test(221,5098 +BOOL into_parent_test(245,5699 +BOOL check_instance(287,6779 +BOOL check_instances(319,7529 +void para_into(341,7989 +void para_into_lit(391,9296 +void para_from_into(442,10931 +Topform para_pos(479,11980 +Topform para_pos2(529,13395 + +../ladr/parautil.c,719 +int Oriented_flag 23,815 +int Renamable_flip_flag 24,893 +void init_paramod(36,1064 +void mark_renamable_flip(55,1452 +BOOL renamable_flip_eq(74,1898 +BOOL renamable_flip_eq_test(95,2333 +void mark_oriented_eq(126,2933 +BOOL oriented_eq(145,3347 +BOOL same_term_structure(168,3792 +void flip_eq(194,4304 +void orient_equalities(218,4878 +BOOL eq_tautology(295,7028 +Term top_flip(320,7539 +void zap_top_flip(343,7906 +Literals literal_flip(358,8065 +void zap_literal_flip(377,8355 +Topform clause_with_new_constant(390,8537 +Topform new_constant(422,9495 +Topform fold_denial(453,10163 +BOOL equational_def_2(486,10939 +int equational_def(504,11256 +Ordertype unfold_order(530,11691 +Topform build_reflex_eq(555,12146 + +../ladr/parse.c,3210 +#define COMMENT_CHAR 23,812 +static char Cons_char 25,838 +static char Quote_char 26,867 +static int Quantifier_precedence 27,898 +static BOOL Parenthesize 29,978 +static BOOL Check_for_illegal_symbols 30,1012 +typedef enum {TOK_UNKNOWN,34,1078 + TOK_ORDINARY,35,1143 + TOK_SPECIAL,36,1190 + TOK_STRING,37,1236 + TOK_COMMENT,38,1280 + TOK_PUNC 39,1326 +} Toktype;Toktype40,1377 +typedef enum {READ_BUF_OK,44,1425 +typedef enum {READ_BUF_OK,READ_BUF_EOF,44,1425 + READ_BUF_ERROR,45,1465 + READ_BUF_ERROR,READ_BUF_QUOTE_ERROR}45,1465 + READ_BUF_ERROR,READ_BUF_QUOTE_ERROR} Read_rc;Read_rc45,1465 +typedef struct token * Token;Token49,1543 +struct token token51,1574 +typedef struct pterm * Pterm;Pterm61,1848 +struct pterm pterm63,1879 +typedef struct tok_pos *Tok_pos;Tok_pos71,2017 +struct tok_pos tok_pos73,2051 +static BOOL Translate_neg_equalities 81,2163 +static Plist Multiple_char_special_syms 82,2211 +#define PTRS_TOKEN 88,2290 +static unsigned Token_gets,89,2336 +static unsigned Token_gets, Token_frees;89,2336 +#define PTRS_PTERM 91,2378 +static unsigned Pterm_gets,92,2424 +static unsigned Pterm_gets, Pterm_frees;92,2424 +Token get_token(101,2534 +void free_token(115,2705 +Pterm get_pterm(128,2865 +void free_pterm(142,3036 +void fprint_parse_mem(161,3408 +void p_parse_mem(193,4220 +void p_tokens(210,4405 +void translate_neg_equalities(238,4950 +Term translate_neg_eq(250,5132 +Term untranslate_neg_eq(276,5697 +void free_pterm_list(302,6270 +void free_token_list(321,6527 +BOOL end_char(340,6788 +BOOL comment_char(352,6920 +BOOL quote_char(364,7067 +BOOL punctuation_char(376,7214 +BOOL ordinary_char(394,7496 +BOOL special_char(410,7749 +BOOL white_char(448,8430 +BOOL all_whitespace(465,8733 +int finish_comment(494,9236 +int read_buf(545,10478 +String_buf max_special_symbol(605,11583 +Token tokenize(653,12639 +int comma_terms(737,14469 +void transfer_comma_term(752,14722 +BOOL quantifier(771,15075 +BOOL ordinary_constant_string(787,15320 +BOOL ordinary_constant(801,15524 +BOOL quant_prefix(816,15755 +Term terms_to_term(836,16173 +void next_token(985,20811 +Term toks_to_set(1005,21119 +Term make_a_list(1022,21443 +Term toks_to_list(1043,21856 +Pterm toks_to_terms(1107,23377 +Term toks_to_term(1226,26058 +void fprint_parse_error(1259,26820 +Term sread_term(1296,27820 +Term read_term(1347,29180 +Term parse_term_from_string(1395,30120 +void arrange_term(1410,30364 +void sb_remove_some_space(1528,33570 +void sb_write_term(1564,34452 +void fwrite_term(1594,35155 +void fwrite_term_nl(1617,35633 +char *process_quoted_symbol(1633,35843 +void remember_multiple_char_special_syms(1661,36447 +void forget_multiple_char_special_syms(1681,36944 +void look_for_illegal_symbols(1701,37433 +void declare_parse_type(1721,37933 +void declare_quantifier_precedence(1744,38457 +void declare_standard_parse_types(1759,38684 +BOOL redeclare_symbol_and_copy_parsetype(1815,40550 +void skip_to_nl(1852,41549 +Plist split_string(1872,41888 +void set_cons_char(1902,42418 +char get_cons_char(1917,42581 +void set_quote_char(1932,42746 +char get_quote_char(1947,42913 +void parenthesize(1962,43079 +void check_for_illegal_symbols(1977,43267 + +../ladr/pindex.c,636 +struct pair_index pair_index23,813 +#define INT_LARGE 35,1259 +#define IN_RANGE(IN_RANGE36,1332 +#define PTRS_PAIR_INDEX 42,1430 +static unsigned Pair_index_gets,43,1486 +static unsigned Pair_index_gets, Pair_index_frees;43,1486 +Pair_index get_pair_index(52,1616 +void free_pair_index(68,1870 +void fprint_pindex_mem(87,2269 +void p_pindex_mem(113,2906 +Pair_index init_pair_index(137,3368 +void zap_pair_index(180,4129 +int pairs_exhausted(210,4697 +void init_pair(224,4894 +void insert_pair_index(265,5757 +void delete_pair_index(304,6619 +void retrieve_pair(401,8657 +void p_pair_index(514,11412 +int pair_already_used(558,12222 + +../ladr/random.c,224 +Term random_term(45,1344 +Term random_nonvariable_term(112,2549 +Term random_complex_term(136,3110 +Ilist random_path(161,3687 +void random_permutation(194,4356 +Topform random_clause(238,5072 +Term random_op_term(265,5604 + +../ladr/resolve.c,1076 +static BOOL Ordered 24,834 +static BOOL Check_instances 25,875 +static int Ur_nucleus_limit 27,917 +static BOOL Initial_nuclei 28,995 +static BOOL Production_mode 29,1075 +static int Res_instance_prunes 31,1117 +void resolution_options(45,1271 +int res_instance_prunes(70,1772 +BOOL unit_check(82,1923 +BOOL pos_hyper_sat_test(95,2118 +BOOL neg_hyper_sat_test(111,2430 +void hyper_sat_atom(127,2738 +void hyper_satellite(191,4489 +void hyper_nucleus(214,5115 +void hyper_resolution(258,6158 +BOOL target_check(276,6562 +void ur_sat_atom(297,7005 +void ur_satellite(364,8858 +void ur_nucleus(385,9332 +void ur_resolution(430,10391 +void xx_res(446,10724 +void binary_resolvent(479,11566 +BOOL binary_parent_test(529,12788 +Topform instantiate_clause(576,14334 +BOOL check_instance(594,14738 +BOOL check_instances(628,15574 +void bin_res_lit(647,15930 +void binary_resolution(681,16847 +void binary_factors(716,17626 +void merge_literals(759,18566 +Topform copy_inference(795,19439 +Topform resolve2(827,20231 +Topform resolve3(883,21518 +Topform xx_resolve2(903,21972 + +../ladr/std_options.c,252 +static int Prolog_style_variables 25,831 +static int Ignore_option_dependencies 26,898 +static int Clocks 27,967 +void init_standard_options(39,1136 +void process_standard_options(58,1559 +int clocks_id(86,2038 +int prolog_style_variables_id(101,2202 + +../ladr/strbuf.c,953 +struct string_buf string_buf25,817 +#define CHUNK_SIZE 30,876 +struct chunk chunk32,900 +typedef struct chunk *Chunk;Chunk37,963 +#define PTRS_CHUNK 43,1022 +static unsigned Chunk_gets,44,1068 +static unsigned Chunk_gets, Chunk_frees;44,1068 +#define PTRS_STRING_BUF 46,1110 +static unsigned String_buf_gets,47,1166 +static unsigned String_buf_gets, String_buf_frees;47,1166 +Chunk get_chunk(56,1286 +void free_chunk(70,1457 +String_buf get_string_buf(86,1654 +void free_string_buf(100,1860 +void fprint_strbuf_mem(119,2259 +void p_strbuf_mem(151,3110 +String_buf init_string_buf(173,3495 +void fprint_sb(191,3762 +void p_sb(218,4235 +void sb_append(238,4549 +void sb_append_char(273,5138 +void sb_replace_char(312,6005 +char sb_char(337,6493 +void sb_cat_copy(363,6960 +void sb_cat(386,7480 +void zap_string_buf(404,7764 +char *sb_to_malloc_string(438,8673 +char *sb_to_malloc_char_array(469,9262 +int sb_size(494,9618 +void sb_append_int(510,9847 + +../ladr/string.c,468 +static char *Float_format 23,813 +BOOL str_ident(36,1027 +char *new_str_copy(53,1325 +BOOL string_member(71,1585 +int which_string_member(92,1983 +BOOL initial_substring(112,2308 +BOOL substring(131,2563 +void reverse_chars(153,2935 +int natural_string(171,3220 +int char_occurrences(192,3479 +char *escape_char(215,3849 +BOOL str_to_int(243,4396 +char *int_to_str(266,4802 +BOOL str_to_double(286,5142 +char *double_to_str(316,5653 +BOOL string_of_repeated(349,6145 + +../ladr/subsume.c,574 +static int Nonunit_subsumption_tests 23,814 +int nonunit_subsumption_tests(35,966 +BOOL subsume_literals(53,1367 +BOOL subsume_bt_literals(87,2046 +BOOL subsumes(133,2991 +BOOL subsumes_bt(158,3532 +Topform forward_subsume(185,4008 +Plist back_subsume(238,5526 +Topform back_subsume_one(294,7039 +void atom_conflict(343,8206 +void unit_conflict_by_index(388,9345 +Topform try_unit_conflict(413,9942 +void unit_delete(445,10778 +Plist back_unit_del_by_index(519,12836 +void simplify_literals(566,13936 +BOOL eq_removable_literal(604,14823 +void simplify_literals2(646,15920 + +../ladr/symbols.c,5368 +struct symbol symbol23,813 +#define SYM_TAB_SIZE 42,1707 +static Plist By_id[44,1736 +static Plist By_sym[45,1804 +static unsigned Symbol_count;47,1874 +static char *True_sym 51,1944 +static char *False_sym 52,1977 +static char *And_sym 53,2010 +static char *Or_sym 54,2042 +static char *Not_sym 55,2074 +static char *Iff_sym 56,2106 +static char *Imp_sym 57,2140 +static char *Impby_sym 58,2173 +static char *All_sym 59,2206 +static char *Exists_sym 60,2240 +static char *Quant_sym 61,2277 +static char *Attrib_sym 65,2359 +static char *Eq_sym 66,2434 +static char *Neq_sym 67,2504 +char *true_sym(79,2670 +char *false_sym(94,2820 +char *and_sym(109,2967 +char *or_sym(124,3107 +char *not_sym(139,3245 +char *iff_sym(154,3386 +char *imp_sym(169,3527 +char *impby_sym(184,3670 +char *all_sym(199,3817 +char *exists_sym(214,3961 +char *quant_sym(229,4118 +char *attrib_sym(244,4273 +char *eq_sym(259,4422 +char *neq_sym(274,4560 +void set_operation_symbol(289,4714 +char *get_operation_symbol(335,6043 +BOOL symbol_in_use(382,7339 +Symbol get_symbol(427,8477 +int new_symnum(457,9065 +unsigned hash_sym(470,9212 +unsigned hash_id(488,9464 +Symbol lookup_by_id(500,9607 +Symbol lookup_by_sym(518,9879 +int str_to_sn(544,10557 +void fprint_syms(580,11386 +void p_syms(609,12018 +void fprint_sym(626,12269 +void sprint_sym(643,12568 +void p_sym(660,12851 +BOOL str_exists(678,13168 +int greatest_symnum(705,13684 +char *sn_to_str(725,14205 +BOOL is_symbol(747,14552 +int sn_to_arity(767,14966 +int sn_to_occurrences(787,15289 +void set_unfold_symbol(807,15626 +BOOL is_unfold_symbol(823,15842 +void declare_aux_symbols(839,16059 +char *parse_type_to_str(862,16573 +void clear_parse_type_for_all_symbols(887,17104 +void clear_parse_type(910,17488 +void check_diff_type_same_prec(932,17865 +void set_parse_type(979,19088 +BOOL binary_parse_type(1023,20238 +BOOL unary_parse_type(1048,20824 +int special_parse_type(1073,21340 +static int Assoc_comm_symbols 1089,21815 +static int Comm_symbols 1090,21873 +void set_assoc_comm(1108,22278 +void set_commutative(1135,22822 +BOOL assoc_comm_symbols(1161,23274 +BOOL comm_symbols(1178,23537 +BOOL is_assoc_comm(1199,24000 +BOOL is_commutative(1221,24518 +static int Eq_symnum 1231,24896 +static int Or_symnum 1232,24922 +static int Not_symnum 1233,24948 +BOOL is_eq_symbol(1248,25234 +int not_symnum(1267,25529 +int or_symnum(1285,25782 +void declare_base_symbols(1302,26006 +static Variable_style Var_style 1315,26405 +void set_variable_style(1328,26616 +Variable_style variable_style(1344,26855 +BOOL variable_name(1362,27200 +void symbol_for_variable(1387,27814 +Ilist variable_symbols(1424,28651 +Ilist remove_variable_symbols(1448,29133 +void set_symbol_type(1471,29682 +Symbol_type get_symbol_type(1489,29974 +BOOL function_symbol(1507,30255 +BOOL relation_symbol(1522,30464 +BOOL function_or_relation_symbol(1537,30686 +void declare_functions_and_relations(1553,30981 +int function_or_relation_sn(1576,31540 +Ilist all_function_symbols(1601,31983 +Ilist all_relation_symbols(1626,32397 +void set_lrpo_status(1655,33045 +void all_symbols_lrpo_status(1673,33373 +Lrpo_status sn_to_lrpo_status(1698,33908 +static BOOL Zero_wt_kb 1708,34288 +void set_kb_weight(1720,34455 +BOOL zero_wt_kb(1750,35093 +int sn_to_kb_wt(1766,35329 +void print_kbo_weights(1785,35579 +static char *Skolem_constant_prefix 1801,36121 +static char *Skolem_function_prefix 1802,36164 +static int Next_skolem_constant 1803,36207 +static int Next_skolem_function 1804,36279 +static BOOL Skolem_check 1805,36351 +void set_skolem(1818,36591 +void skolem_check(1835,36818 +BOOL skolem_ok(1847,36957 +int next_skolem_symbol(1876,37565 +Ilist skolem_symbols(1910,38221 +BOOL is_skolem(1935,38599 +void skolem_reset(1952,38858 +void decommission_skolem_symbols(1970,39178 +void set_skolem_symbols(1995,39590 +static Ilist Preliminary_prec_func 2010,40092 +static Ilist Preliminary_prec_pred 2011,40135 +void set_lex_val(2025,40387 +int sn_to_lex_val(2047,40891 +Ordertype sym_precedence(2066,41309 +Ilist syms_with_lex_val(2099,41911 +BOOL exists_preliminary_precedence(2124,42311 +Ordertype preliminary_lex_compare(2150,42998 +Ordertype lex_compare_base(2189,43968 +Ordertype lex_compare_arity_0123(2278,46207 +Ordertype lex_compare_arity_0213(2299,46616 +void lex_order(2337,47653 +Ilist insert_by_lex_val(2370,48473 +Ilist sort_by_lex_val(2396,48902 +Ilist remove_syms_without_lex_val(2412,49147 +Ilist current_fsym_precedence(2438,49598 +Ilist current_rsym_precedence(2456,49899 +Ilist not_in_preliminary_precedence(2474,50206 +void print_fsym_precedence(2500,50789 +void print_rsym_precedence(2523,51210 +int min_lex_val(2546,51623 +int max_lex_val(2566,51921 +void assign_greatest_precedence(2589,52261 +BOOL has_greatest_precedence(2604,52489 +void lex_insert_after_initial_constants(2619,52729 +Ilist skolem_insert(2650,53369 +void add_skolems_to_preliminary_precedence(2676,53990 +static unsigned Mark_for_new_symbols 2695,54752 +int fresh_symbol(2711,55152 +int gen_new_symbol(2738,55564 +void mark_for_new_symbols(2769,56107 +I2list new_symbols_since_mark(2784,56336 +void add_new_symbols(2806,56707 +void new_constant_properties(2833,57314 +Ilist collect_multiples(2855,57751 +Ilist arity_check(2888,58425 +int symbol_with_string(2905,58718 +void process_skolem_list(2925,59051 +void process_lex_list(2950,59593 +Ilist symnums_of_arity(2992,60712 + +../ladr/term.c,2866 +static Term Shared_variables[59,2360 +#define PTRS_TERM 65,2430 +static unsigned Term_gets,66,2474 +static unsigned Term_gets, Term_frees;66,2474 +static unsigned Arg_mem;68,2514 +Term get_term(77,2655 +void free_term(114,3487 +void fprint_term_mem(135,3937 +void p_term_mem(165,4627 +Term get_variable_term(187,4957 +Term get_rigid_term_like(219,5707 +Term get_rigid_term(240,6162 +Term get_rigid_term_dangerously(274,7100 +void zap_term(295,7514 +BOOL term_ident(319,8002 +Term copy_term(347,8545 +BOOL ground_term(373,9027 +int biggest_variable(398,9454 +int term_depth(423,9882 +int symbol_count(450,10328 +BOOL occurs_in(475,10893 +void fprint_term(499,11283 +void sprint_term(535,11939 +char *term_to_string(573,12641 +void p_term(596,13110 +BOOL all_args_vars(615,13409 +Term build_binary_term(642,13867 +Term build_binary_term_safe(665,14354 +Term build_unary_term(683,14730 +Term build_unary_term_safe(704,15159 +Term subst_term(721,15501 +Term subst_var_term(748,16050 +int greatest_variable(775,16576 +int greatest_symnum_in_term(802,17086 +void upward_term_links(829,17592 +BOOL check_upward_term_links(851,18011 +int occurrences(877,18501 +Term trm_set_vars_recurse(899,18882 +void term_set_variables(945,19996 +Term nat_to_term(978,20634 +Term int_to_term(998,20964 +Term bool_to_term(1020,21308 +Term double_to_term(1038,21642 +int natural_constant_term(1057,21999 +int arg_position(1078,22377 +BOOL is_term(1099,22694 +BOOL is_constant(1115,22935 +char *term_symbol(1132,23223 +BOOL term_to_int(1153,23647 +BOOL term_to_double(1186,24258 +BOOL term_to_number(1207,24666 +BOOL true_term(1230,24990 +BOOL false_term(1245,25161 +BOOL term_to_bool(1263,25461 +I2list symbols_in_term(1289,25893 +Ilist fsym_set_in_term(1310,26218 +Term renum_vars_recurse(1335,26816 +Term set_vars_recurse(1373,27707 +I2list multiset_of_vars(1409,28397 +I2list multiset_vars(1431,28748 +Plist set_of_vars(1447,28955 +Plist set_of_variables(1474,29395 +int number_of_vars_in_term(1490,29631 +Ilist set_of_ivars(1509,29907 +Ilist set_of_ivariables(1536,30404 +BOOL variables_subset(1551,30594 +BOOL variables_multisubset(1571,30945 +Term term_at_pos(1603,31527 +Ilist pos_of_subterm(1622,31811 +Ilist position_of_subterm(1653,32563 +int symbol_occurrences(1674,32923 +BOOL args_distinct_vars(1699,33383 +unsigned hash_term(1750,34178 +BOOL skolem_term(1773,34502 +BOOL contains_skolem_term(1788,34682 +BOOL contains_skolem_function(1813,35067 +Term term0(1839,35480 +Term term1(1855,35692 +Term term2(1873,35949 +BOOL symbol_in_term(1891,36190 +BOOL same_structure(1917,36623 +Plist copy_plist_of_terms(1942,37049 +void zap_plist_of_terms(1966,37448 +BOOL eq_term(1989,37848 +Plist plist_of_subterms(2004,38032 +BOOL tlist_member(2025,38416 +int position_of_term_in_tlist(2045,38717 +BOOL tlist_subset(2065,39018 +BOOL tlist_set(2083,39271 +Plist free_vars_term(2104,39673 + +../ladr/termflag.c,410 +#define TERM_BITS 25,842 +#define SET_BIT(SET_BIT27,893 +#define CLEAR_BIT(CLEAR_BIT28,949 +static int bits_in_use[31,1058 +int claim_term_flag(47,1414 +void release_term_flag(73,1862 +void term_flag_set(99,2602 +void term_flag_clear(119,3045 +BOOL term_flag(139,3489 +int term_flags(162,3944 +Term copy_term_with_flags(180,4242 +Term copy_term_with_flag(209,4822 +void term_flag_clear_recursively(236,5289 + +../ladr/termorder.c,697 +Order_method Ordering_method 24,838 +void assign_order_method(36,1014 +Ordertype term_compare_basic(55,1421 +Ordertype term_compare_ncv(107,2712 +Ordertype term_compare_vcp(155,3913 +Ordertype term_compare_vr(203,5088 +Ordertype flatterm_compare_vr(246,6030 +BOOL lrpo_multiset(291,6920 +BOOL lrpo_lex(306,7244 +BOOL lrpo(354,8491 +void init_kbo_weights(413,9891 +int kbo_weight(454,10743 +BOOL kbo(478,11082 +BOOL term_greater(536,12612 +Ordertype term_order(556,13071 +int flat_kbo_weight(578,13455 +BOOL flat_kbo(601,13814 +BOOL flat_lrpo_multiset(659,15326 +BOOL flat_lrpo_lex(677,15699 +BOOL flat_lrpo(731,16764 +BOOL flat_greater(796,18114 +BOOL greater_multiset_current_ordering(828,18956 + +../ladr/test.c,57 +#define N 22,795 +void compute_args(24,808 +main(35,987 + +../ladr/tlist.c,140 +void zap_tlist(35,1035 +Plist tlist_remove(56,1346 +Plist tlist_union(87,1890 +Ilist constants_in_term(114,2345 +Plist tlist_copy(142,2788 + +../ladr/top_input.c,1344 +typedef struct readlist * Readlist;Readlist29,933 +struct readlist readlist31,970 +static Readlist Input_lists 39,1179 +static Plist Lex_function_list 41,1216 +static Plist Lex_predicate_list 42,1255 +static Plist Skolem_list 43,1295 +static char *Program_name 45,1372 +#define PTRS_READLIST 51,1434 +static unsigned Readlist_gets,52,1486 +static unsigned Readlist_gets, Readlist_frees;52,1486 +Readlist get_readlist(61,1608 +void free_readlist(76,1806 +void fprint_top_input_mem(96,2208 +void p_top_input_mem(122,2844 +void init_standard_ladr(142,3117 +void fatal_input_error(161,3449 +void set_program_name(186,3927 +BOOL condition_is_true(198,4083 +void process_op2(210,4246 +void process_op(249,5317 +void process_redeclare(298,6408 +void execute_unknown_action(333,7283 +void flag_handler(361,7923 +void parm_handler(390,8658 +void process_symbol_list(440,9806 +Readlist readlist_member(468,10675 +Readlist readlist_member_wild(485,10995 +void accept_list(513,11772 +void input_symbols(538,12219 +void symbol_check_and_declare(582,13457 +void read_from_file(697,16616 +void read_all_input(880,22079 +void check_formula_attributes(913,22828 +Plist process_input_formulas(939,23499 +Plist process_demod_formulas(992,25007 +Plist process_goal_formulas(1032,26043 +Term read_commands(1081,27281 +Plist embed_formulas_in_topforms(1175,29840 + +../ladr/topform.c,1249 +#define PTRS_TOPFORM 27,843 +static unsigned Topform_gets,28,893 +static unsigned Topform_gets, Topform_frees;28,893 +Topform get_topform(40,1038 +void free_topform(54,1223 +void fprint_topform_mem(73,1608 +void p_topform_mem(99,2226 +void zap_topform(124,2712 +void fprint_clause(143,3010 +void p_clause(184,3756 +Topform term_to_clause(206,4271 +Topform term_to_topform(233,4712 +Term topform_to_term(269,5528 +Term topform_to_term_without_attributes(304,6331 +void clause_set_variables(338,7176 +void renumber_variables(405,8912 +void term_renumber_variables(453,10002 +Plist renum_vars_map(482,10453 +void upward_clause_links(526,11387 +BOOL check_upward_clause_links(545,11754 +Topform copy_clause(568,12208 +Topform copy_clause_with_flags(589,12614 +Topform copy_clause_with_flag(610,13056 +void inherit_attributes(634,13587 +void gather_symbols_in_topform(653,14047 +void gather_symbols_in_topforms(674,14485 +Ilist fsym_set_in_topforms(691,14791 +Ilist rsym_set_in_topforms(713,15154 +BOOL min_depth(736,15582 +BOOL initial_clause(760,16026 +BOOL negative_clause_possibly_compressed(777,16322 +Term topform_properties(797,16764 +void append_label_attribute(848,18000 +Ordertype cl_id_compare(863,18250 +Ordertype cl_wt_id_compare(883,18545 + +../ladr/tptp_trans.c,562 +void declare_tptp_input_types(152,4779 +void declare_tptp_output_types(198,5945 +Term tptp2_to_ladr_term(250,7493 +Term tptp3_to_ladr_term(301,8629 +Formula tptp_input_to_ladr_formula(418,11841 +void rename_vars_to_upper(459,12889 +Term ladr_term_to_tptp_term(482,13388 +Plist ladr_list_to_tptp_list(564,15539 +Ilist syms_in_form(613,16793 +BOOL good_tptp_sym(667,18225 +BOOL good_ladr_sym(697,18731 +I2list map_for_bad_tptp_syms(712,18909 +I2list map_for_bad_ladr_syms(752,19771 +Term replace_bad_syms_term(793,20657 +Term replace_bad_tptp_syms_form(824,21289 + +../ladr/unify.c,1146 +struct trail trail28,1016 +#define BIND_TR(BIND_TR36,1258 +#define MAX_MULTIPLIERS 41,1456 +static BOOL Multipliers[45,1510 +int next_available_multiplier(54,1669 +#define PTRS_CONTEXT 70,2011 +static unsigned Context_gets,71,2061 +static unsigned Context_gets, Context_frees;71,2061 +#define PTRS_TRAIL 73,2107 +static unsigned Trail_gets,74,2153 +static unsigned Trail_gets, Trail_frees;74,2153 +Context get_context(86,2294 +void free_context(104,2553 +Trail get_trail(120,2853 +void free_trail(134,3044 +void fprint_unify_mem(153,3416 +void p_unify_mem(185,4242 +BOOL unify(241,5800 +BOOL variant(333,7872 +BOOL occur_check(370,8651 +BOOL match(419,10170 +Term apply(477,11462 +Term apply_substitute(516,12530 +Term apply_substitute2(546,13300 +Term apply_demod(585,14289 +void undo_subst(613,14835 +void undo_subst_2(646,15760 +void fprint_context(669,16166 +void p_context(712,17023 +void fprint_trail(728,17281 +void p_trail(751,17676 +BOOL match_weight(767,17874 +Ilist vars_in_trail(824,19130 +Plist context_to_pairs(842,19386 +BOOL empty_substitution(873,19923 +BOOL variable_substitution(893,20202 +BOOL subst_changes_term(919,20673 + +../ladr/weight.c,987 +static Plist Rules;26,874 +static double Constant_weight;28,895 +static double Sk_constant_weight;29,926 +static double Not_weight;30,960 +static double Or_weight;31,986 +static double Prop_atom_weight;32,1011 +static double Variable_weight;33,1043 +static double Nest_penalty;34,1074 +static double Depth_penalty;35,1102 +static double Var_penalty;36,1131 +static double Complexity;37,1158 +static BOOL Not_rules;38,1184 +static BOOL Or_rules;39,1239 +static int Eq_sn;43,1319 +static int Weight_sn;44,1357 +static int Sum_sn;46,1402 +static int Prod_sn;47,1450 +static int Neg_sn;48,1498 +static int Div_sn;49,1546 +static int Max_sn;50,1594 +static int Min_sn;51,1642 +static int Depth_sn;52,1690 +static int Vars_sn;53,1725 +static int Call_sn;54,1759 +static int Avar_sn;55,1793 +BOOL weight_beta_check(64,1912 +BOOL weight_rule_check(100,2720 +void init_weight(125,3224 +int apply_depth(193,4832 +double weight_calc(217,5280 +double weight(301,7546 +double clause_weight(358,8787 + +../ladr/weight2.c,186 +#define IMAX(IMAX39,1413 +int char_array_ident(52,1612 +int char_array_find(69,1954 +double complexity_1(88,2316 +double test1(141,3647 +double call_weight(166,4182 +int main(179,4426 + +../ladr/xproofs.c,350 +void check_parents_and_uplinks_in_proof(36,975 +Topform xx_res2(65,1751 +void xx_simp2(108,2678 +Topform factor(134,3290 +void merge1(171,4145 +Topform proof_id_to_clause(201,4773 +int greatest_id_in_proof(222,5088 +Plist expand_proof(251,5910 +void renumber_proof(539,14887 +Plist copy_and_renumber_proof(568,15492 +Plist proof_to_xproof(585,15778 diff --git a/adder4.stab b/adder4.stab new file mode 100644 index 0000000..7d3fd67 --- /dev/null +++ b/adder4.stab @@ -0,0 +1,8 @@ +// Prove that A+0=A with a ripple-carry adder +//expected: unsat +/\i=1..n ((S_i <-> (A_i (+) B_i (+) C_i)) /\ (C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i))) +/\ ~C_1 +/\ /\i=1..n ~B_i +/\ \/i=1..n (A_i (+) S_i) + +// vim:ft=regstab diff --git a/arith5.in b/arith5.in new file mode 100644 index 0000000..d7abb54 --- /dev/null +++ b/arith5.in @@ -0,0 +1,42 @@ +%assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 1300). +set(raw). +%predicate_order([ Y, XpY, S5, X1, S6, S7, S8, S9, T1, T2, T3, T4, T5, $T1$, N, M1, M2, M4, S1, S2, S3, S4, $M2$$, $M3$, $M4$$, $M2$, $M4$, $M1$, $M2$$$, $M3$$, $M4$$%$, $X1$, $Y$, M3 ]). +set(binary_resolution). +%set(random_given). +%set(print_gen). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). + +( ( N(X) | -$X1$(X) ) & ( N(X) | -$Y$(X) ) ) & ( M1(s(0)) & ( N(X) | S1(s(X)) ) ) & ( M2(s(0)) & -$M2$(s(0)) & $M2$$(s(0)) & ( N(X) | S2(s(X)) ) ) & ( M3(s(0)) & $M3$(s(0)) & ( N(X) | S3(s(X)) ) ) & ( -M4(s(0)) & -$M4$(s(0)) & $M4$$(s(0)) & ( N(X) | S4(s(X)) ) ) & ( ( N(X) | S5(s(X)) ) & -T1(s(0)) ) & ( ( N(X) | T2(X) ) & T2(0) & ( N(X) | S6(s(X)) ) ) & ( ( N(X) | T3(X) ) & T3(0) & ( N(X) | S7(s(X)) ) ) & ( ( ( N(X) | T4(X) ) & T4(0) & ( N(X) | S8(X) ) ) ) & ( ( ( N(X) | T5(X) ) & T5(0) & ( N(X) | S9(s(X)) ) ) ) . +S1(0). + +S2(0) . +S3(0) . + +S4(0) <-> $T . +S5(0) <-> $T . +S6(0) <-> $T . +S7(0) <-> $T . +S8(0) <-> $T . +S9(0) <-> $T . +M1(s(X)) <-> $M1$(X) . +M2(s(X)) <-> $M2$(X) . +$M2$(s(X)) <-> $M2$$(X) . +$M2$$(s(X)) <-> $M2$$$(X) . +M3(s(X)) <-> $M3$(X) . +$M3$(s(X)) <-> $M3$$(X) . +M4(s(X)) <-> $M4$(X) . +$M4$(s(X)) <-> $M4$$(X) . +$M4$$(s(X)) <-> $M4$$$(X) . +T1(s(X)) <-> $T1$(X) . +X1(s(X)) <-> $X1$(X) . +Y(s(X)) <-> $Y$(X) . + +end_of_list. \ No newline at end of file diff --git a/arith5.txt b/arith5.txt new file mode 100644 index 0000000..d7abb54 --- /dev/null +++ b/arith5.txt @@ -0,0 +1,42 @@ +%assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 1300). +set(raw). +%predicate_order([ Y, XpY, S5, X1, S6, S7, S8, S9, T1, T2, T3, T4, T5, $T1$, N, M1, M2, M4, S1, S2, S3, S4, $M2$$, $M3$, $M4$$, $M2$, $M4$, $M1$, $M2$$$, $M3$$, $M4$$%$, $X1$, $Y$, M3 ]). +set(binary_resolution). +%set(random_given). +%set(print_gen). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). + +( ( N(X) | -$X1$(X) ) & ( N(X) | -$Y$(X) ) ) & ( M1(s(0)) & ( N(X) | S1(s(X)) ) ) & ( M2(s(0)) & -$M2$(s(0)) & $M2$$(s(0)) & ( N(X) | S2(s(X)) ) ) & ( M3(s(0)) & $M3$(s(0)) & ( N(X) | S3(s(X)) ) ) & ( -M4(s(0)) & -$M4$(s(0)) & $M4$$(s(0)) & ( N(X) | S4(s(X)) ) ) & ( ( N(X) | S5(s(X)) ) & -T1(s(0)) ) & ( ( N(X) | T2(X) ) & T2(0) & ( N(X) | S6(s(X)) ) ) & ( ( N(X) | T3(X) ) & T3(0) & ( N(X) | S7(s(X)) ) ) & ( ( ( N(X) | T4(X) ) & T4(0) & ( N(X) | S8(X) ) ) ) & ( ( ( N(X) | T5(X) ) & T5(0) & ( N(X) | S9(s(X)) ) ) ) . +S1(0). + +S2(0) . +S3(0) . + +S4(0) <-> $T . +S5(0) <-> $T . +S6(0) <-> $T . +S7(0) <-> $T . +S8(0) <-> $T . +S9(0) <-> $T . +M1(s(X)) <-> $M1$(X) . +M2(s(X)) <-> $M2$(X) . +$M2$(s(X)) <-> $M2$$(X) . +$M2$$(s(X)) <-> $M2$$$(X) . +M3(s(X)) <-> $M3$(X) . +$M3$(s(X)) <-> $M3$$(X) . +M4(s(X)) <-> $M4$(X) . +$M4$(s(X)) <-> $M4$$(X) . +$M4$$(s(X)) <-> $M4$$$(X) . +T1(s(X)) <-> $T1$(X) . +X1(s(X)) <-> $X1$(X) . +Y(s(X)) <-> $Y$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Arrays/x1tab.in b/benchmarks/Arrays/x1tab.in new file mode 100644 index 0000000..43ec4ee --- /dev/null +++ b/benchmarks/Arrays/x1tab.in @@ -0,0 +1,32 @@ +%set(raw). +assign(max_given, 30). +set(binary_resolution). +set(paramodulation). +set(ordered_para). +%assign(order, kbo). +set(print_gen). +set(ordered_res). +%assign(max_depth, 4). +%assign(max_literals,4). +set(superind). +set(random_given). +%set(breadth_first). +assign(literal_selection, none). +clear(predicate_elim). + +formulas(sos). +select(store(T, X , V) , X ) = V. +N(A) | select(store( t(A), ip , a) , is) != select(tp(A),is) . +X = Y | select(store(T, X , V) , Y ) = select(T,Y). + + + +t(0) =tt. + tp(0) = store(tt, ip, a). +t(s(J)) = store(t(J), i(J) , e(J)). +tp(s(J)) = store(tp(J), i(J) , e(J)). +i(J) != ip. + +end_of_list. + + diff --git a/benchmarks/Arrays/x6tab.in b/benchmarks/Arrays/x6tab.in new file mode 100644 index 0000000..b7f96ab --- /dev/null +++ b/benchmarks/Arrays/x6tab.in @@ -0,0 +1,31 @@ +set(prolog_style_variables). +assign(max_given, 2300). +%set(raw). +set(index_flat). +set(print_gen). +set(superind). +clear(sat). +%set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +t(0) = tz. + store(t(U),b(U),c(U)) = t(s(U)) . +-(b(U) = a). +select(store(T, X , V) , X) = V. +x = y | select(store(T, X , V) , Y) = select(T,Y). +select(tz, a)=d. +N(U) | select(t(U), a) != d. + + +end_of_list. diff --git a/benchmarks/FirstOrderExamples/FD.in b/benchmarks/FirstOrderExamples/FD.in new file mode 100644 index 0000000..bafd2db --- /dev/null +++ b/benchmarks/FirstOrderExamples/FD.in @@ -0,0 +1,26 @@ +%Simple example from Spass-FD +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). + +G(s(0), 0). +G(X,Y) -> G(s(X),s(Y)). +N(X) | -H(X,X). +H(X,Y) <-> G(s(X),Y). + +end_of_list. \ No newline at end of file diff --git a/benchmarks/FirstOrderExamples/FD_addition.in b/benchmarks/FirstOrderExamples/FD_addition.in new file mode 100644 index 0000000..24d6b4d --- /dev/null +++ b/benchmarks/FirstOrderExamples/FD_addition.in @@ -0,0 +1,28 @@ +%Simple example from Spass-FD +set(prolog_style_variables). +assign(max_given, 2300). +%set(raw). +set(index_flat). +%set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). + +0 + Y = Y . + X+Y != Z | s(Z) = s(X) + Y . +N(X) | -(X + 0 = X). + + +end_of_list. \ No newline at end of file diff --git a/benchmarks/FirstOrderExamples/FD_even.in b/benchmarks/FirstOrderExamples/FD_even.in new file mode 100644 index 0000000..4a1b6fc --- /dev/null +++ b/benchmarks/FirstOrderExamples/FD_even.in @@ -0,0 +1,29 @@ +%Simple example from Spass-FD +% Sat +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +N(X) | -even(X). +even(0). +even(X) -> even1(s(X)). +even(s(X)) <-> even1(X). + + +end_of_list. \ No newline at end of file diff --git a/benchmarks/FirstOrderExamples/Furst2.in b/benchmarks/FirstOrderExamples/Furst2.in new file mode 100644 index 0000000..dca36c2 --- /dev/null +++ b/benchmarks/FirstOrderExamples/Furst2.in @@ -0,0 +1,134 @@ +%set(raw). +assign(max_given, 1000). +set(binary_resolution). +set(paramodulation). +set(ordered_para). +assign(order, kbo). +%set(print_gen). +set(ordered_res). +assign(max_depth, 4). +assign(max_literals,6). +assign(max_vars, 4). +set(superind). +set(random_given). +%set(rank_given). +%set(breadth_first). +assign(literal_selection, none). +clear(predicate_elim). + +formulas(assumptions). + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Inductive lemma +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +N(y) | (sch(c,y) & -lem1(c,y)). +% lem1_disj(x,y) is the disjunction of the p(j)*s4(x)=x +% for j=0 to y-1 + +-lem1_disj(x,s(y)) | (p(y)*s4(x)=x) | lem1_disj(x,y). +lem1_disj(x,s(y)) | -(p(y)*s4(x)=x). +lem1_disj(x,s(y)) | -(lem1_disj(x,y)). +-lem1_disj(x,0). + +% lem1(x,y) holds iff s(0) lem1_disj(x,y) + +-lem1(x,y) | -(s(0)lem1(x,r) +% base case OK +%sch(x,0). +%-lem1(c,0). + +% inductive case OK +%sch(c,s®). +%-lem1(c,s®). + + +% inductive proof of lem1(s(0)+(ts(0)*x),s(r))=> lem2(x,r) + +% base case OK +% lem1(s(0)+(ts(0)*c),s(0)). +% -lem2(c,0). + +% inductive case OK +%lem1(s(0)+(ts(0)*c),s(s(r))). +%-lem2(c,s(r)). +%-lem1(s(0)+(ts(0)*x),s(r)) | lem2(x,r). + + + + +% basic axioms + +0+x=x. +x*y=y*x. +0 0 +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% Proof OK % +%%%%%%%%%%%%% + +% ts(x) is the product of prime numbers +% p(0)...p(x-1) + +ts(s(x)) = ts(x)*p(s(x)). +ts(0)=p(0). + +%% Induction proof for ts(x) + +% base case +%-(0 P(f(a,b)). +Si(s(X)) <-> P(f(a,Si(X))). + + + +-P(cst). +f(a,b) = d. +f(a,d) = cst. +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/Iterme2.in b/benchmarks/FirstOrderExamples/Iterme2.in new file mode 100644 index 0000000..c92d0e8 --- /dev/null +++ b/benchmarks/FirstOrderExamples/Iterme2.in @@ -0,0 +1,34 @@ +set(prolog_style_variables). +% generates N(s(0)) but not N(0) because of f(a,b) = d ... +%set(raw). +assign(max_given, 200). +set(binary_resolution). +set(paramodulation). +set(ordered_para). +%assign(order, kbo). +%set(print_gen). +set(ordered_res). +%assign(max_depth, 4). +%assign(max_literals,4). +set(superind). +clear(sat). +set(rank_given). +%set(breadth_first). +assign(literal_selection, none). +clear(predicate_elim). +formulas(sos). + +p(X) | -q(X,Y) . +q(nil, X). +q(cons(X,Y), X) | -q(Y,X) . +Si(0) = nil. +Si(s(X)) = cons(a,Si(X)). + +N(X) | -p(Si(X)). + + + +-P(cst). +f(a,b) = d. +f(a,d) = cst. +end_of_list. diff --git a/benchmarks/FirstOrderExamples/ItermeBisOK.in b/benchmarks/FirstOrderExamples/ItermeBisOK.in new file mode 100644 index 0000000..be37125 --- /dev/null +++ b/benchmarks/FirstOrderExamples/ItermeBisOK.in @@ -0,0 +1,34 @@ +set(prolog_style_variables). + +set(raw). +assign(max_given, 30). +set(binary_resolution). +%set(paramodulation). +set(ordered_para). +assign(order, kbo). +set(print_gen). +set(ordered_res). +assign(max_depth, 5). +%assign(max_literals,4). +set(superind). +predicate_order([ N, Si, q, p ]). + +clear(sat). +set(rank_given). +%set(breadth_first). +assign(literal_selection, none). +clear(predicate_elim). +formulas(sos). +N(X) | -Si(X,Y) | -p(Y). +p(X) | -q(X,Y) . + +q(nil, X). +q(cons(X,Y), X) | -q(Y,X) . + +Si(0,nil). +Si(s(X), cons(a,Y)) | -Si(X,Y). + + +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/TPTP_Counter.in b/benchmarks/FirstOrderExamples/TPTP_Counter.in new file mode 100644 index 0000000..cd54e2b --- /dev/null +++ b/benchmarks/FirstOrderExamples/TPTP_Counter.in @@ -0,0 +1,97 @@ + %To complete +forall([X0, X1, X10, X11, X12, X13, X2, X3, X4, X5, X6, X7, X8, X9], +or( not(p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,s0)), + p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,s1))), +rule1 ). + + +forall([X0, X1, X10, X11, X12, X2, X3, X4, X5, X6, X7, X8, X9], +or( not(p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,s0,s1)), + p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,s1,s0))), +rule2 ). + + +forall([X0, X1, X10, X11, X2, X3, X4, X5, X6, X7, X8, X9], +or( not(p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,s0,s1,s1)), + p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,s1,s0,s0))), +rule3 ). + + +forall([X0, X1, X10, X2, X3, X4, X5, X6, X7, X8, X9], +or( not(p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,s0,s1,s1,s1)), + p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,s1,s0,s0,s0))), +rule4 ). + + +forall([X0, X1, X2, X3, X4, X5, X6, X7, X8, X9], +or( not(p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,s0,s1,s1,s1,s1)), + p(X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,s1,s0,s0,s0,s0))), +rule5 ). + + +forall([X0, X1, X2, X3, X4, X5, X6, X7, X8], +or( not(p(X0,X1,X2,X3,X4,X5,X6,X7,X8,s0,s1,s1,s1,s1,s1)), + p(X0,X1,X2,X3,X4,X5,X6,X7,X8,s1,s0,s0,s0,s0,s0))), +rule6 ). + + +forall([X0, X1, X2, X3, X4, X5, X6, X7], +or( not(p(X0,X1,X2,X3,X4,X5,X6,X7,s0,s1,s1,s1,s1,s1,s1)), + p(X0,X1,X2,X3,X4,X5,X6,X7,s1,s0,s0,s0,s0,s0,s0))), +rule7 ). + + +forall([X0, X1, X2, X3, X4, X5, X6], +or( not(p(X0,X1,X2,X3,X4,X5,X6,s0,s1,s1,s1,s1,s1,s1,s1)), + p(X0,X1,X2,X3,X4,X5,X6,s1,s0,s0,s0,s0,s0,s0,s0))), +rule8 ). + + +forall([X0, X1, X2, X3, X4, X5], +or( not(p(X0,X1,X2,X3,X4,X5,s0,s1,s1,s1,s1,s1,s1,s1,s1)), + p(X0,X1,X2,X3,X4,X5,s1,s0,s0,s0,s0,s0,s0,s0,s0))), +rule9 ). + + +forall([X0, X1, X2, X3, X4], +or( not(p(X0,X1,X2,X3,X4,s0,s1,s1,s1,s1,s1,s1,s1,s1,s1)), + p(X0,X1,X2,X3,X4,s1,s0,s0,s0,s0,s0,s0,s0,s0,s0))), +rule10 ). + + +forall([X0, X1, X2, X3], +or( not(p(X0,X1,X2,X3,s0,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1)), + p(X0,X1,X2,X3,s1,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0))), +rule11 ). + + +forall([X0, X1, X2], +or( not(p(X0,X1,X2,s0,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1)), + p(X0,X1,X2,s1,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0))), +rule12 ). + + +forall([X0, X1], +or( not(p(X0,X1,s0,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1)), + p(X0,X1,s1,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0))), +rule13 ). + + +forall([X0], +or( not(p(X0,s0,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1)), + p(X0,s1,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0))), +rule14 ). + + +or( not(p(s0,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1)), + p(s1,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0,s0)), +rule15 ). + +end_of_list. + + + + +-p(s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1,s1). + +end_of_list. \ No newline at end of file diff --git a/benchmarks/FirstOrderExamples/TPTP_simple.in b/benchmarks/FirstOrderExamples/TPTP_simple.in new file mode 100644 index 0000000..63636ca --- /dev/null +++ b/benchmarks/FirstOrderExamples/TPTP_simple.in @@ -0,0 +1,30 @@ +%Simple example from Spass-FD +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). + +formulas(sos). +c0in(c0Pair(V0x,V0x,tc0Comb0Ocomb,tc0Comb0Ocomb),c0Comb0Oparcontract,tc0prod(tc0Comb0Ocomb,tc0Comb0Ocomb)). + + + + + + c0in(c0Pair(v0x,v0xb,tc0Comb0Ocomb,tc0Comb0Ocomb),c0Comb0Oparcontract,tc0prod(tc0Comb0Ocomb,tc0Comb0Ocomb) ). + + + +-c0in(c0Pair(v0xb,V0U,tc0Comb0Ocomb,tc0Comb0Ocomb),c0Comb0Oparcontract,tc0prod(tc0Comb0Ocomb,tc0Comb0Ocomb)) | + -c0in(c0Pair(v0x,V0U,tc0Comb0Ocomb,tc0Comb0Ocomb),c0Comb0Oparcontract,tc0prod(tc0Comb0Ocomb,tc0Comb0Ocomb)). +end_of_list. + diff --git a/benchmarks/FirstOrderExamples/TPTP_simple.txt b/benchmarks/FirstOrderExamples/TPTP_simple.txt new file mode 100644 index 0000000..72fd613 --- /dev/null +++ b/benchmarks/FirstOrderExamples/TPTP_simple.txt @@ -0,0 +1,32 @@ +%Simple example from Spass-FD +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +c_in(c_Pair(V_x,V_x,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) + + + + + + c_in(c_Pair(v_x,v_xb,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb) ) + + + +-c_in(c_Pair(v_xb,V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) | + -c_in(c_Pair(v_x,V_U,tc_Comb_Ocomb,tc_Comb_Ocomb),c_Comb_Oparcontract,tc_prod(tc_Comb_Ocomb,tc_Comb_Ocomb)) +end_of_list. + diff --git a/benchmarks/FirstOrderExamples/limite.in b/benchmarks/FirstOrderExamples/limite.in new file mode 100644 index 0000000..505ef0f --- /dev/null +++ b/benchmarks/FirstOrderExamples/limite.in @@ -0,0 +1,30 @@ +set(prolog_style_variables). +assign(max_given, 20). +%set(raw). + +set(index_flat). +set(print_gen). +set(superind). +set(cycle2). +set(random_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + + +formulas(sos). +S(0) = 1. +S(s(X)) = c * S(X) . +c < 1. +-(c < 0 ). +( (c < 1) & -(X = 0)) -> c * X < X. +-(Y < 0) -> -(Y * X < 0). +(C < B & X < Y) -> C * X < B * Y. +N(X) | -(X < n0(X)) & -(S(X) < 0 ). +end_of_list. \ No newline at end of file diff --git a/benchmarks/FirstOrderExamples/listes.in b/benchmarks/FirstOrderExamples/listes.in new file mode 100644 index 0000000..a45ad44 --- /dev/null +++ b/benchmarks/FirstOrderExamples/listes.in @@ -0,0 +1,29 @@ + + +set(prolog_style_variables). +assign(max_given, 1000). +%set(raw). +set(index_flat). +%set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +assign(start_rank, 0). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +set(ordered_para). +%set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. + +formulas(sos). +lengthAtLeast(L,X) <-> (X = 0 | exists C exists Lp exists Xp ( L = cons(C,Lp) & X = s(Xp) & lengthAtLeast(Lp,Xp) ) ). +nth(X,L,M) <-> exists Lp L = cons(Y,Lp) & (M = s(0) & X = Y) | exists Mp (M = s(Mp) & nth(X,Lp,Mp)). +N(X) | lengthAtLeast(L,X). +N(0). +N(X) | -nth(Y,L,X). +end_of_list. diff --git a/benchmarks/FirstOrderExamples/sat_addition.in b/benchmarks/FirstOrderExamples/sat_addition.in new file mode 100644 index 0000000..3f46bce --- /dev/null +++ b/benchmarks/FirstOrderExamples/sat_addition.in @@ -0,0 +1,30 @@ +%Simple example from Spass-FD +% Sat +set(prolog_style_variables). +assign(max_given, 20). +%set(raw). +set(index_flat). +set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +N(X) | somme(X) != s(0). +somme(0) = s(0). +A = somme(X) -> somme(s(X)) = s(A). + + + + +end_of_list. \ No newline at end of file diff --git a/benchmarks/FirstOrderExamples/x10serie.in b/benchmarks/FirstOrderExamples/x10serie.in new file mode 100644 index 0000000..101ed80 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x10serie.in @@ -0,0 +1,25 @@ +assign(max_weight, 30). +%set(raw). +set(print_gen). +assign(order, kbo). +set(binary_resolution). +clear(neg_binary_resolution). +assign(literal_selection, none). +clear(predicate_elim). +predicate_order([N,!=,=]). +list(kbo_weights). + s = 3. +end_of_list. +formulas(sos). + f(0,r)=1. + minus(1)=0. + f(s(x),r)=r*f(x,r). + sigma(0) = q. + sigma(s(x))=sigma(x)+(f(x,r)*q). + N(s(x)) | sigma(x)*minus(q) != q*minus(f(s(x),r)) . + + +end_of_list. + + + diff --git a/benchmarks/FirstOrderExamples/x11somme.in b/benchmarks/FirstOrderExamples/x11somme.in new file mode 100644 index 0000000..82bc8c2 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x11somme.in @@ -0,0 +1,31 @@ +assign(max_weight, 30). +%set(raw). +%set(print_gen). +assign(order, kbo). +assign(max_given, 100). +set(binary_resolution). +clear(neg_binary_resolution). +assign(literal_selection, none). +clear(predicate_elim). +%predicate_order([N,=]). +list(kbo_weights). + s = 3. +end_of_list. +formulas(sos). + X+Y=Y+X. + X*Y=Y*X. + X*1=X. + 1+X=s(X). +%s(0)=1. +%s(X)=X+1. + sigma(1)=1. +minus(X,X)=0. +minus(X+Y,Y)=X. +2*minus(X,Y)=minus(2*X,2*Y). +minus(sigma(s(X)),s(X))=sigma(X). + N(X) | 2*sigma(X) != X*s(X) . + + +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x12Fur.in b/benchmarks/FirstOrderExamples/x12Fur.in new file mode 100644 index 0000000..3f29b67 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x12Fur.in @@ -0,0 +1,22 @@ +assign(max_weight, 100). +set(prolog_style_variables). +set(binary_resolution). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). +-R(s(X)) | R(X). + 0 < t(S). +fs(S) | -(1 < 1+(t(S)*X)) | fs1(S,S,X). +0 < X * Y | 0 < Y | 0 < X. + R(S1) | -fs1(S1,S,X). % fs1(S,X) est vide si S>r + -R(S1) | -fs1(S1,S,X) | p(s(S1)) * s4(1+(t(S)*X))= 1+(t(S) * X ) | fs1(s(S1),S,X). +N(S) | -fs(S). + +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x13Prop1.in b/benchmarks/FirstOrderExamples/x13Prop1.in new file mode 100644 index 0000000..f668821 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x13Prop1.in @@ -0,0 +1,24 @@ +% UNSAT OK +assign(max_weight, 100). +set(prolog_style_variables). +set(raw). +set(binary_resolution). +set(ordered_res). +set(superind). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). +p(0). +-p(X) | q(X). +-q(X) | -q(s(X)). +q(X) | q(s(X)). +N(X) |-q(X). +N(X) | -q(s(X)). +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x15.in b/benchmarks/FirstOrderExamples/x15.in new file mode 100644 index 0000000..1e31807 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x15.in @@ -0,0 +1,14 @@ +set(prolog_style_variables). +clear(predicate_elim). +set(raw). +set(binary_resolution). +set(print_gen). +assign(max_given, 10). +formulas(sos). +p(0,f(a,b)). +-p(X,f(Y,Z)) | p(s(X),f(Z,Y)) | p(s(X),f(Y,Z)). +N(X) | -p(X,f(a,Z)) . +N(X) | -p(X,f(Z,a)) . +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x18CeresCvetan.in b/benchmarks/FirstOrderExamples/x18CeresCvetan.in new file mode 100644 index 0000000..446982e --- /dev/null +++ b/benchmarks/FirstOrderExamples/x18CeresCvetan.in @@ -0,0 +1,79 @@ +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 41. +% +% % number of calls to fixpoint : 4 +% S_init : +% (15: [ -p(f(g(v0,a))) if n = s(v0) ]. +% 21: [ r(v0) if n = s(v0) ]. +% 20: [ -p(g(v0,v1)) | p(f(g(v0,v1))) if n = s(v0) ]. +% 34: [ -p(g(v0,a)) if n = s(v0) ]. +% ) +% S_loop : +% (45: [ -p(g(v0,a)) if n = s(s(v0)) ]. +% 23: [ -p(g(v0,v1)) | p(f(g(v0,v1))) if n = s(s(v0)) ]. +% 24: [ r(v0) if n = s(s(v0)) ]. +% 38: [ -p(f(g(v0,a))) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (17: [ n = 0 ]. +% 33: [ n = s(0) ]. +% 44: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=41. Generated=78. Kept=56. proofs=1. +% Usable=31. Sos=13. Demods=2. Limbo=0, Disabled=22. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=8. Back_subsumed=11. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=2 (0 lex), Back_demodulated=1. Back_unit_deleted=0. +% Demod_attempts=611. Demod_rewrites=15. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=89. Nonunit_bsub_feature_tests=90. +% Megabytes=0.12. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== +set(prolog_style_variables). +assign(max_given, 1200). + +%set(raw). +%set(lightest_first). +%set(print_gen). +%set(back_subsume). +%set(back_demod). +%set(cac_redundancy). +assign(max_depth, 4). + +%set(ordered_para). +%set(paramodulation). +%set(binary_resolution). + +assign(literal_selection, none). +clear(predicate_elim). +assign(order, kbo). +%set(cycle2). +%predicate_order([N,p,g,r,q, =]). +list(kbo_weights). + s = 10. +end_of_list. + +formulas(sos). +(r(0) & p(Z)) -> p(f(g(0,Z))). +-q(0). +-r(s(X)) | r(X). +(r(s(X)) & p(g(X,Z )) ) -> p(f(g(X,Z))). +-q(s(X)) | r(s(X)). +p(a). +-(q(s(X)) & p(f(g(X, a))) ). +g(0,Z) = Z. +g(s(X), Z) = f(g(X,Z)). +N(X) | q(X). +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x19Complexity_10.in b/benchmarks/FirstOrderExamples/x19Complexity_10.in new file mode 100644 index 0000000..adfa8b0 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x19Complexity_10.in @@ -0,0 +1,66 @@ +% Unsat OK +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.01) seconds. +% % Given clauses 84. +% +% % number of calls to fixpoint : 4 +% S_init : +% (65: [ g(t(v0)) != t(0) if n = s(v0) ]. +% 66: [ t(0) != t(v0) if n = s(v0) ]. +% ) +% S_loop : +% (124: [ t(0) != t(v0) if n = s(s(v0)) ]. +% 88: [ g(t(v0)) != t(0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (41: [ n = 0 ]. +% 67: [ n = s(0) ]. +% 106: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=84. Generated=258. Kept=172. proofs=1. +% Usable=83. Sos=76. Demods=4. Limbo=0, Disabled=26. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=86. Back_subsumed=10. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=4 (0 lex), Back_demodulated=3. Back_unit_deleted=0. +% Demod_attempts=2112. Demod_rewrites=36. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=1419. Nonunit_bsub_feature_tests=573. +% Megabytes=0.30. +% User_CPU=0.01, System_CPU=0.01, Wall_clock=0. +% +% ============================== end of statistics ===================== +% + +%assign(max_seconds, 1). +%set(raw). +set(back_subsume). +set(back_demod). +set(cac_redundancy). +%clear(auto_inference). +set(prolog_style_variables). +%set(print_gen). +%set(index_flat). +%set(cycle2). +set(binary_resolution). +set(paramodulation). +set(ordered_res). +set(ordered_para). +assign(max_given, 100). +assign(literal_selection, none). +%predicate_order([N,>]). + +formulas(sos). +N(X) | (t(X) != f(a,T1,T2,T3,T4,T5,T6,T7,T8,T9) & t(X) != f(T1, a, T2,T3,T4,T5,T6,T7,T8,T9) & t(X) != f(T1,T2,a,T3,T4,T5,T6,T7,T8,T9) & t(X) != f(T1,T2,T3, a,T4,T5,T6,T7,T8,T9) & t(X) != f(T1,T2,T3,T4,a,T5,T6,T7,T8,T9) & t(X) != f(T1,T2,T3,T4,T5,a,T6,T7,T8,T9) & t(X) != f(T1,T2,T3,T4,T5,T6,a,T7,T8,T9) & t(X) != f(T1,T2,T3,T4,T5,T6,T7,a,T8,T9) & t(X) != f(T1,T2,T3,T4,T5,T6,T7,T8,a,T9) & t(X) != f(T1,T2,T3,T4,T5,T6,T7,T8,T9,a)). + +t(X)!=f(Z,T1,T2,T3,T4,T5,T6,T7,T8,T9) | g(t(X)) = f(T1,Z,T2,T3,T4,T5,T6,T7,T8,T9). +t(s(X)) = g(t(X)). +t(0) = f(a,T1,T2,T3,T4,T5,T6,T7,T8,T9). +end_of_list. + diff --git a/benchmarks/FirstOrderExamples/x19Complexity_2.in b/benchmarks/FirstOrderExamples/x19Complexity_2.in new file mode 100644 index 0000000..f34f123 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x19Complexity_2.in @@ -0,0 +1,22 @@ +% Unsat OK +%assign(max_seconds, 1). +%set(raw). +set(back_subsume). +%clear(auto_inference). +set(prolog_style_variables). +%set(print_gen). +set(binary_resolution). + +set(paramodulation). +set(ordered_para). +%clear(ordered_res). +assign(max_given, 500). +assign(literal_selection, none). + +formulas(sos). +N(X) | (t(X) != f(a,Z) & t(X) != f(Z,a) ). +t(X)!=f(Z,Y) | g(t(X)) = f(Y,Z). +t(s(X)) = g(t(X)). +t(0) = f(a,Z). +end_of_list. + diff --git a/benchmarks/FirstOrderExamples/x19Complexity_3.in b/benchmarks/FirstOrderExamples/x19Complexity_3.in new file mode 100644 index 0000000..67bedc4 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x19Complexity_3.in @@ -0,0 +1,19 @@ +% Unsat OK + +set(prolog_style_variables). +%set(print_gen). +set(binary_resolution). + +set(paramodulation). +set(ordered_para). +%clear(ordered_res). +assign(max_given, 500). +assign(literal_selection, none). +formulas(sos). +N(X) | (t(X) != f(a,Z,T) & t(X) != f(Z,a,T) & t(X) != f(Z,T,a)). +t(X) != f(Z,Y,T) | g(t(X)) = f(Y,T,Z). +t(s(X)) = g(t(X)). + +t(0) = f(a,Z,T). +end_of_list. + diff --git a/benchmarks/FirstOrderExamples/x19Complexity_3e.in b/benchmarks/FirstOrderExamples/x19Complexity_3e.in new file mode 100644 index 0000000..3560838 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x19Complexity_3e.in @@ -0,0 +1,32 @@ +% Unsat OK + + +set(raw). +set(back_subsume). +set(back_demod). +set(cac_redundancy). +%clear(auto_inference). +set(prolog_style_variables). +set(print_gen). +%set(breadth_first). +assign(order, kbo). + +%set(ordered_para). +%set(paramodulation). +set(binary_resolution). +set(ordered_res). +assign(max_given, 50). +set(rank_given). +assign(start_rank, 1). +predicate_order([ N, e ]). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. +formulas(sos). +N(X) | (-e(X,a,X2,X3) & -e(X, X2,a,X3 ) & -e(X, X2,X3,a) ). +-e(X, X1,X2,X3) | (e(s(X) ,X1,X2,X3) | e(s(X), X2,X1,X3 ) | e(s(X), X3,X2,X1) | e(s(X) ,X1,X3,X2) ). +e(0, a,b,c). +end_of_list. + diff --git a/benchmarks/FirstOrderExamples/x1Triv.in b/benchmarks/FirstOrderExamples/x1Triv.in new file mode 100644 index 0000000..e03de79 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x1Triv.in @@ -0,0 +1,18 @@ +% Unsat OK +assign(max_weight, 15). +set(raw). +set(superind). +set(print_gen). +set(binary_resolution). +set(ordered_res). +%clear(neg_binary_resolution). +assign(literal_selection, none). +%set(hyper_resolution). +clear(predicate_elim). +formulas(sos). + ( N(x) | -P(x,y) ) & (-P(x,y) | P(s(x),f(y))) & P(0,a). + +end_of_list. + + + diff --git a/benchmarks/FirstOrderExamples/x1tab.in b/benchmarks/FirstOrderExamples/x1tab.in new file mode 100644 index 0000000..e427333 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x1tab.in @@ -0,0 +1,32 @@ +set(raw). +assign(max_given, 30). +set(binary_resolution). +set(paramodulation). +set(ordered_para). +%assign(order, kbo). +set(print_gen). +set(ordered_res). +%assign(max_depth, 4). +%assign(max_literals,4). +set(superind). +set(random_given). +%set(breadth_first). +assign(literal_selection, none). +clear(predicate_elim). + +formulas(sos). +select(store(T, X , V) , X ) = V. +N(A) | select(store( t(A), ip , a) , is) != select(tp(A),is) . +X = Y | select(store(T, X , V) , Y ) = select(T,Y). + + + +t(0) =tt. + tp(0) = store(tt, ip, a). +t(s(J)) = store(t(J), i(J) , e(J)). +tp(s(J)) = store(tp(J), i(J) , e(J)). +i(J) != ip. + +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x20prod2.txt b/benchmarks/FirstOrderExamples/x20prod2.txt new file mode 100644 index 0000000..2578a8d --- /dev/null +++ b/benchmarks/FirstOrderExamples/x20prod2.txt @@ -0,0 +1,49 @@ +set(prolog_style_variables). +assign(max_given, 2300). +%set(raw). +set(index_flat). +%set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +%set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. +%Je pense qu'on peut facilement trouver des exemples intéressants suivant %ce principe, avec pas mal de variations possibles et pouvant être %compliquées autant qu'on veut. Un exemple très simple: +%p_i(x,y): code le fait que la ressource x est associée au client y à %l'instant i +%q(x,y): le fait que le client demande la ressource x +%r_i(x,y): code le fait que la ressource x a déjà été associée au client y %(avant l'instant i) + +%On peut considérer un nbre arbitraire (mais fixé, sf à considérer des %schémas avec deux paramètres...) de clients et de ressources. +formulas(sos). + + +%On peut ensuite définir une politique d'attribution comme un ensemble de %clauses du premier ordre et utiliser le calcul pour vérifier ses %propriétés. Par exemple, on peut supposer que les clients sont totalement %ordonnés et que toute ressource r est affectée en priorité au client %maximal qui la demande. Puis on vérifie que tout client finit par obtenir %la ressource qu'il souhaite. +a > b. +p(0,a,r1). +p(0,b,r2). +-r(I,X,T) | -q(X,T). + +N(I) | -p(I,X,r1) & -p(I,X,r1). + + + +%-(p(I,X,R) & (T != R)) | -p(I,X,T). + +-( (X > Z) & q(X,R) & q(Z,R) & -r(I,R,T) ) | p(I,X,R). + +-r(I,X,T) | -q(X,T). + +-(p(I,X,R) & -q(Z,R) ) | p(s(I),X,R). + +-(p(I,X,R) & (q(Z,R) & X > Z )) | p(s(I),X,R). +%N(I) | -p(I,Z,R). + +end_of_list. diff --git a/benchmarks/FirstOrderExamples/x20production.in b/benchmarks/FirstOrderExamples/x20production.in new file mode 100644 index 0000000..29d1336 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x20production.in @@ -0,0 +1,47 @@ +set(prolog_style_variables). +assign(max_given, 2300). +%set(raw). +set(index_flat). +%set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +%set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. +%Je pense qu'on peut facilement trouver des exemples int�ressants suivant %ce principe, avec pas mal de variations possibles et pouvant �tre %compliqu�es autant qu'on veut. Un exemple tr�s simple: +%p_i(x,y): code le fait que la ressource x est associ�e au client y � %l'instant i +%q(x,y): le fait que le client demande la ressource x +%r_i(x,y): code le fait que la ressource x a d�j� �t� associ�e au client y %(avant l'instant i) + +%On peut consid�rer un nbre arbitraire (mais fix�, sf � consid�rer des %sch�mas avec deux param�tres...) de clients et de ressources. +formulas(sos). + + +%On peut ensuite d�finir une politique d'attribution comme un ensemble de %clauses du premier ordre et utiliser le calcul pour v�rifier ses %propri�t�s. Par exemple, on peut supposer que les clients sont totalement %ordonn�s et que toute ressource r est affect�e en priorit� au client %maximal qui la demande. Puis on v�rifie que tout client finit par obtenir %la ressource qu'il souhaite. +a > b. +b > c. +a > c. +p(0,a,r1). +p(0,b,r2). +p(0,c,r3). +-(p(I,X,R) & (T != R)) | -p(I,X,T). + +-( (X > Z) & q(X,R) & q(Z,R) & -r(I,R,T) ) | p(I,X,R). + +-r(I,X,T) | -q(X,T). + +-(p(I,X,R) & -q(Z,R) ) | p(s(I),X,R). + +-(p(I,X,R) & (q(Z,R) & X > Z )) | p(s(I),X,R). +N(I) | -p(I,Z,R). + +end_of_list. + diff --git a/benchmarks/FirstOrderExamples/x6tab.in b/benchmarks/FirstOrderExamples/x6tab.in new file mode 100644 index 0000000..1749f76 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x6tab.in @@ -0,0 +1,16 @@ +%Unsat NOT OK +assign(max_weight, 100). +set(binary_resolution). +set(print_gen). +clear(neg_binary_resolution). +assign(literal_selection, none). +predicate_order([ N, = ]). +clear(process_initial_sos). +clear(predicate_elim). +formulas(sos). +t(s(u)) = store(store(t(u),i(u),select(t(u),j(u))),j(u), select(t(u),i(u))). +select(t(0), 3)=6. +N(u) | select(t(u), y) != 6. +x != y | select(store(r, x , v) , y ) = v. +x = y | select(store(r, x , v) , y ) = select(r,y). +end_of_list. diff --git a/benchmarks/FirstOrderExamples/x7Fur.in b/benchmarks/FirstOrderExamples/x7Fur.in new file mode 100644 index 0000000..ea9c9e7 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x7Fur.in @@ -0,0 +1,69 @@ +% Unsat OK +% ts > 0. +% ============================== PROOF ================================= +% +% % Proof 1 at 0.06 (+ 0.01) seconds. +% % Given clauses 68. +% +% % number of calls to fixpoint : 1 +% S_init : +% (1: [ ->(f(v0),0) if n = v0 ]. +% ) +% S_loop : +% (20: [ ->(f(v0),0) if n = s(v0) ]. +% ) +% The empty clauses : +% (18: [ n = 0 ]. +% 25: [ n = s(0) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=68. Generated=1176. Kept=1100. proofs=1. +% Usable=59. Sos=1029. Demods=3. Limbo=0, Disabled=21. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=75. Back_subsumed=11. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=3 (0 lex), Back_demodulated=1. Back_unit_deleted=0. +% Demod_attempts=18643. Demod_rewrites=47. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=36. Nonunit_bsub_feature_tests=46. +% Megabytes=1.86. +% User_CPU=0.06, System_CPU=0.01, Wall_clock=0. +% +% ============================== end of statistics ===================== + +%assign(max_weight, 100). +%set(raw). +assign(max_given, 100). +set(binary_resolution). +set(paramodulation). +%set(ordered_para). +assign(order, kbo). +%set(print_gen). +set(ordered_res). +set(superind). +set(cycle1). +assign(literal_selection, none). +%clear(predicate_elim). + +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). +N(x) |-( f(x) > 0). +f(s(x)) = *(f(x),p(x)). +-(x>0) | -(y>0) | x*y > 0. +f(0)=1. +p(y) > 1. +1 > 0. +-(x > 1) | x > 0. +-(x>0) | *(1,x) > 0. +*(1,x)=x. + +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x8ACO.in b/benchmarks/FirstOrderExamples/x8ACO.in new file mode 100644 index 0000000..0b26573 --- /dev/null +++ b/benchmarks/FirstOrderExamples/x8ACO.in @@ -0,0 +1,34 @@ +% Unsat OK +% X1 * � * Xn = Xn * � X1 +%assign(max_weight, 14). +%assign(max_seconds, 1). +assign(max_given, 600). +clear(back_subsume). +%set(raw). +set(superind). +assign(start_rank, 0). +set(cycle2). +%set(rank_given). +%set(print_gen). +set(binary_resolution). +set(paramodulation). +set(ordered_res). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). +N(x) | p(x) != q(x). +p(0) = 1. +q(0)=1. +p(s(x)) = p(x)*a(x). +q(s(x)) = a(x)*q(x). +*(x,1)=x. +*(1,x)=x. +x*y = u*v | x != u | y!=v. +x*y=y*x. +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x8ACOe.in b/benchmarks/FirstOrderExamples/x8ACOe.in new file mode 100644 index 0000000..c636aee --- /dev/null +++ b/benchmarks/FirstOrderExamples/x8ACOe.in @@ -0,0 +1,51 @@ +assign(max_weight, 30). +%set(raw). +%clear(auto_inference). + +%clear(ordered_res). + + +set(raw). +assign(max_given, 180). +assign(order, kbo). +set(random_given). +%assign(max_literals, 5). +%assign(max_depth, 5). +clear(back_subsume). +assign(max_megs, 1). +set(binary_resolution). +set(ordered_res). +assign(literal_selection, none). +predicate_order([N,e,p,q]). +clear(predicate_elim). +list(kbo_weights). + s = 25. + e = 2. + p = 3. + q = 4. +end_of_list. +%list(actions). + + % given=50 -> set(random_given). + % given=50 -> set(print_gen). + + +%end_of_list. +formulas(sos). + + +N(x) | -p(x,u) | -q(x,v) | -e(u,v). + +p(s(x),a(x)*y) | -p(x,y). +q(s(x),y*a(x)) | -q(x,y). + +e(x*y,u*v) | -e(x,u) | -e(y,v). +e(x*y,u*v) | -e(x,v) | -e(y,u). +p(0,1). +q(0,1). +e(x,x). +e(x*1,x). +e(x,x*1). +end_of_list. + + diff --git a/benchmarks/FirstOrderExamples/x9paire.in b/benchmarks/FirstOrderExamples/x9paire.in new file mode 100644 index 0000000..98a2dcb --- /dev/null +++ b/benchmarks/FirstOrderExamples/x9paire.in @@ -0,0 +1,22 @@ +% UNSAT NOT YET +assign(max_weight, 15). +%set(raw). +%set(print_gen). +set(binary_resolution). +clear(neg_binary_resolution). +assign(literal_selection, none). +clear(predicate_elim). + +formulas(sos). +p(s(zk),i(y),s(s(x))) | -p(zk,i(y),x). +all wj( p(s(zk),wj , s(s(x))) | -p(zk,wj,x) | wj = i(y)). +p(0,a,b). +even(b). +N(y) | -p(y,a,x) | -even(x). +even(s(s(x))) | -even(x). +-even( s(s(x)) )| even(x). +even(0). +-even(s(0)). +end_of_list. + + diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder1.in b/benchmarks/Regstab/bitvectors/carrypropagate/adder1.in new file mode 100644 index 0000000..4302a00 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder1.in @@ -0,0 +1,58 @@ +% A + 0 = A +% ============================== PROOF ================================= +% +% % Proof 1 at 0.76 (+ 0.04) seconds. +% % Given clauses 516. +% +% % number of calls to fixpoint : 3 +% S_init : +% (49: [ S1(v0) if n = s(v0) ]. +% 90: [ S2(v0) if n = s(v0) ]. +% 866: [ S3(v0) | $C$(v0) if n = s(v0) ]. +% ) +% S_loop : +% (1152: [ $C$(v0) | S3(v0) if n = s(s(v0)) ]. +% 1015: [ S2(v0) if n = s(s(v0)) ]. +% 992: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (113: [ n = 0 ]. +% 864: [ n = s(0) ]. +% 1219: [ n = s(s(0)) ]. +% ) max_rank 2 +% +% ============================== end of proof ========================== +% + + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 900). +set(raw). +set(back_subsume). +set(rank_given). +set(index_flat). +%set(cycle1). +set(random_loopdet). +assign(start_rank, 1). +%set(cycle2). +%set(print_gen). +set(binary_resolution). +%clear(ordered_res). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +%list(kbo_weights). +%s = 3. +%end_of_list. +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( N(X) | S2(X) ) & ( N(X) | S3(X) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A(s(X)) <-> B(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( A(s(X)) & B(s(X)) ) | ( A(s(X)) | B(s(X)) ) & C(s(X)) ) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & -B(s(X)) ) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | -(A(s(X)) <-> S(s(X))) ) . +C(s(X)) <-> $C$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder1.stab b/benchmarks/Regstab/bitvectors/carrypropagate/adder1.stab new file mode 100644 index 0000000..90cedf0 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder1.stab @@ -0,0 +1,14 @@ +// Prove that A+0=A with a *carry-propagate* adder +//expected: unsat + +let Propagate(i) := A_i \/ B_i in +let Generate(i) := A_i /\ B_i in +let Carry(i) := C_i+1 <-> (Generate(i) \/ Propagate(i) /\ C_i) in +let Sum(i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Adder := /\i=1..n (Sum(i) /\ Carry(i)) /\ ~C_1 in +let NullB := /\i=1..n ~B_i in +let Conclusion := /\i=1..n (A_i <-> S_i) in + +Adder() /\ NullB() /\ ~Conclusion() + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder2.in b/benchmarks/Regstab/bitvectors/carrypropagate/adder2.in new file mode 100644 index 0000000..2d88a49 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder2.in @@ -0,0 +1,77 @@ +%Commutativity of the carry-propagate adder +% ============================== PROOF ================================= +% +% % Proof 1 at 0.09 (+ 0.02) seconds. +% % Given clauses 456. +% +% % number of calls to fixpoint : 4 +% S_init : +% (73: [ S1(v0) if n = s(v0) ]. +% 74: [ S2(v0) if n = s(v0) ]. +% 178: [ S3(v0) | $CP$(v0) | $C$(v0) if n = s(v0) ]. +% 215: [ S3(v0) | -$CP$(v0) | -$C$(v0) if n = s(v0) ]. +% ) +% S_loop : +% (394: [ S3(v0) | -$CP$(v0) | -$C$(v0) if n = s(s(v0)) ]. +% 337: [ S3(v0) | $CP$(v0) | $C$(v0) if n = s(s(v0)) ]. +% 81: [ S2(v0) if n = s(s(v0)) ]. +% 80: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (75: [ n = 0 ]. +% 214: [ n = s(0) ]. +% 333: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=456. Generated=3487. Kept=510. proofs=1. +% Usable=290. Sos=9. Demods=0. Limbo=0, Disabled=274. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=1332. Back_subsumed=211. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=3252. Nonunit_bsub_feature_tests=744. +% Megabytes=0.89. +% User_CPU=0.09, System_CPU=0.02, Wall_clock=0. +% +% ============================== end of statistics ===================== +% + + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 2000). +set(raw). + +set(index_flat). +set(print_gen). +set(superind). +%set(cycle2). +set(random_loopdet). +set(random_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( ( N(X) | S2(X) ) & -CP(s(0)) ) & ( ( N(X) | S3(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( A1(s(X)) | A2(s(X)) ) & C(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( SP(s(X)) <-> -( - (A2(s(X)) <-> A1(s(X)) ) <-> CP(s(X))) ) & ( $CP$(s(X)) <-> ( ( A2(s(X)) & A1(s(X)) ) | ( A2(s(X)) | A1(s(X)) ) & CP(s(X))) ) ) ) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | -(S(s(X)) <-> SP(s(X))) ) . +C(s(X)) <-> $C$(X) . +CP(s(X)) <-> $CP$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder2.stab b/benchmarks/Regstab/bitvectors/carrypropagate/adder2.stab new file mode 100644 index 0000000..c1bcb22 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder2.stab @@ -0,0 +1,13 @@ +// Commutativity of the carry-propagate adder +//expected: unsat + +let Propagate(A,B,i) := A_i \/ B_i in +let Generate(A,B,i) := A_i /\ B_i in +let Carry(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ Propagate(A,B,i) /\ C_i) in +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in +let Equal(X,Y) := /\i=1..n (X_i <-> Y_i) in + +Adder(A1,A2,S,C,n) /\ Adder(A2,A1,S',C',n) /\ ~Equal(S,S') + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder3.in b/benchmarks/Regstab/bitvectors/carrypropagate/adder3.in new file mode 100644 index 0000000..f30f6b3 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder3.in @@ -0,0 +1,94 @@ + % Associativity of the carry-propagate adder +% ============================== PROOF ================================= +% +% % Proof 1 at 0.68 (+ 0.03) seconds. +% % Given clauses 2280. +% +% % number of calls to fixpoint : 3 +% S_init : +% (135: [ S1(v0) if n = s(v0) ]. +% 140: [ S2(v0) if n = s(v0) ]. +% 141: [ S3(v0) if n = s(v0) ]. +% 142: [ S4(v0) if n = s(v0) ]. +% 795: [ S5(v0) | -$C2P$(v0) | -$C$(v0) | $C2$(v0) | $C1$(v0) if n = s(v0) ]. +% 797: [ S5(v0) | -$C2P$(v0) | $C$(v0) | $C2$(v0) | -$C1$(v0) if n = s(v0) ]. +% 798: [ S5(v0) | $C2P$(v0) | -$C$(v0) | -$C2$(v0) | $C1$(v0) if n = s(v0) ]. +% 800: [ S5(v0) | $C2P$(v0) | $C$(v0) | -$C2$(v0) | -$C1$(v0) if n = s(v0) ]. +% 802: [ S5(v0) | $C2P$(v0) | $C$(v0) | $C2$(v0) | $C1$(v0) if n = s(v0) ]. +% 794: [ S5(v0) | -$C2P$(v0) | -$C$(v0) | -$C2$(v0) | -$C1$(v0) if n = s(v0) ]. +% ) +% S_loop : +% (2723: [ S5(v0) | -$C2P$(v0) | -$C$(v0) | -$C2$(v0) | -$C1$(v0) if n = s(s(v0)) ]. +% 2726: [ S5(v0) | $C2P$(v0) | $C$(v0) | $C2$(v0) | $C1$(v0) if n = s(s(v0)) ]. +% 2724: [ S5(v0) | $C2P$(v0) | $C$(v0) | -$C2$(v0) | -$C1$(v0) if n = s(s(v0)) ]. +% 2722: [ S5(v0) | $C2P$(v0) | -$C$(v0) | -$C2$(v0) | $C1$(v0) if n = s(s(v0)) ]. +% 2721: [ S5(v0) | -$C2P$(v0) | $C$(v0) | $C2$(v0) | -$C1$(v0) if n = s(s(v0)) ]. +% 2720: [ S5(v0) | -$C2P$(v0) | -$C$(v0) | $C2$(v0) | $C1$(v0) if n = s(s(v0)) ]. +% 831: [ S4(v0) if n = s(s(v0)) ]. +% 818: [ S3(v0) if n = s(s(v0)) ]. +% 817: [ S2(v0) if n = s(s(v0)) ]. +% 816: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (147: [ n = 0 ]. +% 850: [ n = s(0) ]. +% 2770: [ n = s(s(0)) ]. +% ) max_rank 2 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=2280. Generated=52066. Kept=2755. proofs=1. +% Usable=1342. Sos=40. Demods=0. Limbo=0, Disabled=1492. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=48568. Back_subsumed=1373. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=9248. Nonunit_bsub_feature_tests=4197. +% Megabytes=6.30. +% User_CPU=0.68, System_CPU=0.03, Wall_clock=1. +% +% ============================== end of statistics ===================== +% + + +set(prolog_style_variables). +assign(max_given, 3300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +%set(random_loopdet). +assign(start_rank,1). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | S1(X) ) & -C1(s(0)) ) & ( ( N(X) | S2(X) ) & -C(s(0)) ) & ( ( N(X) | S3(X) ) & -C2P(s(0)) ) & ( ( N(X) | S4(X) ) & -C2(s(0)) ) & ( ( N(X) | S5(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( B1(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C1(s(X))) ) & ( $C1$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( A1(s(X)) | A2(s(X)) ) & C1(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( S(s(X)) <-> -( - (B1(s(X)) <-> A3(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( B1(s(X)) & A3(s(X)) ) | ( B1(s(X)) | A3(s(X)) ) & C(s(X))) ) ) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & ( ( SP(s(X)) <-> -( - (A1(s(X)) <-> B2(s(X)) ) <-> C2P(s(X))) ) & ( $C2P$(s(X)) <-> ( ( A1(s(X)) & B2(s(X)) ) | ( A1(s(X)) | B2(s(X)) ) & C2P(s(X))) ) ) ) . +S4(0) <-> $T . +S4(s(X)) <-> ( S4(X) & ( ( B2(s(X)) <-> -( - (A2(s(X)) <-> A3(s(X)) ) <-> C2(s(X))) ) & ( $C2$(s(X)) <-> ( ( A2(s(X)) & A3(s(X)) ) | ( A2(s(X)) | A3(s(X)) ) & C2(s(X))) ) ) ) . +S5(0) <-> $F . +S5(s(X)) <-> ( S5(X) | -(S(s(X)) <-> SP(s(X))) ) . +C1(s(X)) <-> $C1$(X) . +C(s(X)) <-> $C$(X) . +C2P(s(X)) <-> $C2P$(X) . +C2(s(X)) <-> $C2$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder3.stab b/benchmarks/Regstab/bitvectors/carrypropagate/adder3.stab new file mode 100644 index 0000000..527927f --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder3.stab @@ -0,0 +1,15 @@ +// Associativity of the carry-propagate adder +//expected: unsat + +let Propagate(A,B,i) := A_i \/ B_i in +let Generate(A,B,i) := A_i /\ B_i in +let Carry(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ Propagate(A,B,i) /\ C_i) in +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in +let Equal(X,Y) := /\i=1..n (X_i <-> Y_i) in + +Adder(A1,A2,B1,C1,n) /\ Adder(B1,A3,S,C1',n) +/\ Adder(A1,B2,S',C2',n) /\ Adder(A2,A3,B2,C2,n) +/\ ~Equal(S,S') + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder4.in b/benchmarks/Regstab/bitvectors/carrypropagate/adder4.in new file mode 100644 index 0000000..7bbfa28 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder4.in @@ -0,0 +1,53 @@ + +%============================== PROOF ================================= + +% Proof 1 at 0.02 (+ 0.00) seconds. +% Given clauses 67. + +% Si : +% (14: N(v0) | S3(v0). +%12: N(v0) | S2(v0). +%10: N(v0) | S1(v0). +%) +% Sij : + %(377: S3(v0) | N(s(v0)). +%122: S2(v0) | N(s(v0)). +%73: S1(v0) | N(s(v0)). +%) +% The empty clauses : +% (376: N(0). +%487: N(s(0)). +%) max_rank 2 + +%============================== end of proof ==========================assign(max_weight, 15). +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( ( N(X) | S2(X) ) & -CP(s(0)) ) & ( ( N(X) | S3(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( A1(s(X)) | A2(s(X)) ) & C(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( SP(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> CP(s(X))) ) & ( $CP$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( - A1(s(X)) <-> A2(s(X)) ) & CP(s(X))) ) ) ) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | -(S(s(X)) <-> SP(s(X))) ) . +C(s(X)) <-> $C$(X) . +CP(s(X)) <-> $CP$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder4.stab b/benchmarks/Regstab/bitvectors/carrypropagate/adder4.stab new file mode 100644 index 0000000..3a5095b --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder4.stab @@ -0,0 +1,17 @@ +// The propagation can be expressed both as a OR or as a XOR. +// We show that both are equivalent. +//expected: unsat + +let PropagateOR(A,B,i) := A_i \/ B_i in +let PropagateXOR(A,B,i) := A_i (+) B_i in +let Generate(A,B,i) := A_i /\ B_i in +let CarryOR(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ PropagateOR(A,B,i) /\ C_i) in +let CarryXOR(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ PropagateXOR(A,B,i) /\ C_i) in +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let AdderOR(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ CarryOR(A,B,C,i)) /\ ~C_1 in +let AdderXOR(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ CarryXOR(A,B,C,i)) /\ ~C_1 in +let Equal(X,Y) := /\i=1..n (X_i <-> Y_i) in + +AdderOR(A1,A2,S,C,n) /\ AdderXOR(A1,A2,S',C',n) /\ ~Equal(S,S') + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder5.in b/benchmarks/Regstab/bitvectors/carrypropagate/adder5.in new file mode 100644 index 0000000..eead7c4 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder5.in @@ -0,0 +1,77 @@ +%Equivalence between the ripple-carry and the carry-propagate adders +%expected: unsat +%theorem proved +% ============================== PROOF ================================= +% +% % Proof 1 at 0.06 (+ 0.01) seconds. +% % Given clauses 352. +% +% % number of calls to fixpoint : 4 +% S_init : +% (73: [ S1(v0) if n = s(v0) ]. +% 74: [ S2(v0) if n = s(v0) ]. +% 164: [ S3(v0) | -$CP$(v0) | -$C$(v0) if n = s(v0) ]. +% 166: [ S3(v0) | $CP$(v0) | $C$(v0) if n = s(v0) ]. +% ) +% S_loop : +% (298: [ S3(v0) | $CP$(v0) | $C$(v0) if n = s(s(v0)) ]. +% 296: [ S3(v0) | -$CP$(v0) | -$C$(v0) if n = s(s(v0)) ]. +% 169: [ S2(v0) if n = s(s(v0)) ]. +% 168: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (75: [ n = 0 ]. +% 176: [ n = s(0) ]. +% 308: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=352. Generated=1786. Kept=434. proofs=1. +% Usable=203. Sos=9. Demods=0. Limbo=0, Disabled=285. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=1268. Back_subsumed=222. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=1093. Nonunit_bsub_feature_tests=680. +% Megabytes=0.73. +% User_CPU=0.06, System_CPU=0.01, Wall_clock=0. +% +% ============================== end of statistics ===================== + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( ( N(X) | S2(X) ) & -CP(s(0)) ) & ( ( N(X) | S3(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( A1(s(X)) | A2(s(X)) ) & C(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( SP(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> CP(s(X))) ) & ( $CP$(s(X)) <-> (A1(s(X)) & A2(s(X)) | CP(s(X)) & A1(s(X)) | CP(s(X)) & A2(s(X))) ) ) ) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | -(S(s(X)) <-> SP(s(X))) ) . +C(s(X)) <-> $C$(X) . +CP(s(X)) <-> $CP$(X) . + +end_of_list. + diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/adder5.stab b/benchmarks/Regstab/bitvectors/carrypropagate/adder5.stab new file mode 100644 index 0000000..f1f4895 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/adder5.stab @@ -0,0 +1,15 @@ +// Equivalence between the ripple-carry and the carry-propagate adders +//expected: unsat + +let Propagate(A,B,i) := A_i \/ B_i in +let Generate(A,B,i) := A_i /\ B_i in +let PCarry(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ Propagate(A,B,i) /\ C_i) in +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let CPAdder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ PCarry(A,B,C,i)) /\ ~C_1 in +let RCarry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let RCAdder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ RCarry(A,B,C,i)) /\ ~C_1 in +let Equal(X,Y) := /\i=1..n (X_i <-> Y_i) in + +CPAdder(A1,A2,S,C,n) /\ RCAdder(A1,A2,S',C',n) /\ ~Equal(S,S') + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/bis.stab b/benchmarks/Regstab/bitvectors/carrypropagate/bis.stab new file mode 100644 index 0000000..d6f9c3b --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/bis.stab @@ -0,0 +1,2 @@ +//expected: sat +P_0 diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder1.stab b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder1.stab new file mode 100644 index 0000000..90e079e --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder1.stab @@ -0,0 +1,14 @@ +// Prove that A+0=A with a *carry-propagate* adder +//expected: sat + +let Propagate(i) := A_i \/ B_i in +let Generate(i) := A_i /\ B_i in +let Carry(i) := C_i+1 <-> (Generate(i) \/ Propagate(i) /\ C_i) in +let Sum(i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Adder := /\i=1..n (Sum(i) /\ Carry(i)) /\ ~C_1 in +let NullB := /\i=1..n ~B_i in +let Conclusion := /\i=1..n (A_i <-> S_i) in + +Adder() /\ NullB() | n>=5 + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder2.in b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder2.in new file mode 100644 index 0000000..3173650 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder2.in @@ -0,0 +1,33 @@ +%Commutativity of the carry-propagate adder + + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 200). +set(raw). + +set(index_flat). +set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( ( N(X) | S2(X) ) & -CP(s(0)) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( A1(s(X)) | A2(s(X)) ) & C(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( SP(s(X)) <-> -( - (A2(s(X)) <-> A1(s(X)) ) <-> CP(s(X))) ) & ( $CP$(s(X)) <-> ( ( A2(s(X)) & A1(s(X)) ) | ( A2(s(X)) | A1(s(X)) ) & CP(s(X))) ) ) ) . + +C(s(X)) <-> $C$(X) . +CP(s(X)) <-> $CP$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder2.stab b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder2.stab new file mode 100644 index 0000000..4bb6d8d --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder2.stab @@ -0,0 +1,13 @@ +// Commutativity of the carry-propagate adder +//expected: sat + +let Propagate(A,B,i) := A_i \/ B_i in +let Generate(A,B,i) := A_i /\ B_i in +let Carry(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ Propagate(A,B,i) /\ C_i) in +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in +let Equal(X,Y) := /\i=1..n (X_i <-> Y_i) in + +Adder(A1,A2,S,C,n) /\ Adder(A2,A1,S',C',n) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder3.in b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder3.in new file mode 100644 index 0000000..e58ad24 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder3.in @@ -0,0 +1,37 @@ + % Associativity of the carry-propagate adder +% sat +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +assign(start_rank,1). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | S1(X) ) & -C1(s(0)) ) & ( ( N(X) | S2(X) ) & -C(s(0)) ) & ( ( N(X) | S3(X) ) & -C2P(s(0)) ) & ( ( N(X) | S4(X) ) & -C2(s(0)) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( B1(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C1(s(X))) ) & ( $C1$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( A1(s(X)) | A2(s(X)) ) & C1(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( S(s(X)) <-> -( - (B1(s(X)) <-> A3(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( B1(s(X)) & A3(s(X)) ) | ( B1(s(X)) | A3(s(X)) ) & C(s(X))) ) ) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & ( ( SP(s(X)) <-> -( - (A1(s(X)) <-> B2(s(X)) ) <-> C2P(s(X))) ) & ( $C2P$(s(X)) <-> ( ( A1(s(X)) & B2(s(X)) ) | ( A1(s(X)) | B2(s(X)) ) & C2P(s(X))) ) ) ) . +S4(0) <-> $T . +S4(s(X)) <-> ( S4(X) & ( ( B2(s(X)) <-> -( - (A2(s(X)) <-> A3(s(X)) ) <-> C2(s(X))) ) & ( $C2$(s(X)) <-> ( ( A2(s(X)) & A3(s(X)) ) | ( A2(s(X)) | A3(s(X)) ) & C2(s(X))) ) ) ) . + +C1(s(X)) <-> $C1$(X) . +C(s(X)) <-> $C$(X) . +C2P(s(X)) <-> $C2P$(X) . +C2(s(X)) <-> $C2$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder3.stab b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder3.stab new file mode 100644 index 0000000..74ceabb --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder3.stab @@ -0,0 +1,14 @@ +// Associativity of the carry-propagate adder +//expected: sat + +let Propagate(A,B,i) := A_i \/ B_i in +let Generate(A,B,i) := A_i /\ B_i in +let Carry(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ Propagate(A,B,i) /\ C_i) in +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in +let Equal(X,Y) := /\i=1..n (X_i <-> Y_i) in + +Adder(A1,A2,B1,C1,n) /\ Adder(B1,A3,S,C1',n) +/\ Adder(A1,B2,S',C2',n) /\ Adder(A2,A3,B2,C2,n) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder4.in b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder4.in new file mode 100644 index 0000000..9dcb519 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder4.in @@ -0,0 +1,32 @@ + +==========================assign(max_weight, 15). +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( ( N(X) | S2(X) ) & -CP(s(0)) ). +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( A1(s(X)) | A2(s(X)) ) & C(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( SP(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> CP(s(X))) ) & ( $CP$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( - A1(s(X)) <-> A2(s(X)) ) & CP(s(X))) ) ) ) . + +C(s(X)) <-> $C$(X) . +CP(s(X)) <-> $CP$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder4.stab b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder4.stab new file mode 100644 index 0000000..e4e11f7 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder4.stab @@ -0,0 +1,17 @@ +// The propagation can be expressed both as a OR or as a XOR. +// We show that both are equivalent. +//expected: sat + +let PropagateOR(A,B,i) := A_i \/ B_i in +let PropagateXOR(A,B,i) := A_i (+) B_i in +let Generate(A,B,i) := A_i /\ B_i in +let CarryOR(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ PropagateOR(A,B,i) /\ C_i) in +let CarryXOR(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ PropagateXOR(A,B,i) /\ C_i) in +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let AdderOR(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ CarryOR(A,B,C,i)) /\ ~C_1 in +let AdderXOR(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ CarryXOR(A,B,C,i)) /\ ~C_1 in +let Equal(X,Y) := /\i=1..n (X_i <-> Y_i) in + +AdderOR(A1,A2,S,C,n) /\ AdderXOR(A1,A2,S',C',n) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder5.in b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder5.in new file mode 100644 index 0000000..d97e589 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder5.in @@ -0,0 +1,36 @@ +%Equivalence between the ripple-carry and the carry-propagate adders +%expected: sat +%theorem proved + + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( ( N(X) | S2(X) ) & -CP(s(0)) ). +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ( ( A1(s(X)) & A2(s(X)) ) | ( A1(s(X)) | A2(s(X)) ) & C(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( SP(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> CP(s(X))) ) & ( $CP$(s(X)) <-> (A1(s(X)) & A2(s(X)) | CP(s(X)) & A1(s(X)) | CP(s(X)) & A2(s(X))) ) ) ) . +N(0). +C(s(X)) <-> $C$(X) . +CP(s(X)) <-> $CP$(X) . + +end_of_list. + diff --git a/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder5.stab b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder5.stab new file mode 100644 index 0000000..5a2fa09 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/carrypropagate/sat/adder5.stab @@ -0,0 +1,15 @@ +// Equivalence between the ripple-carry and the carry-propagate adders +//expected: sat + +let Propagate(A,B,i) := A_i \/ B_i in +let Generate(A,B,i) := A_i /\ B_i in +let PCarry(A,B,C,i) := C_i+1 <-> (Generate(A,B,i) \/ Propagate(A,B,i) /\ C_i) in +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let CPAdder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ PCarry(A,B,C,i)) /\ ~C_1 in +let RCarry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let RCAdder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ RCarry(A,B,C,i)) /\ ~C_1 in +let Equal(X,Y) := /\i=1..n (X_i <-> Y_i) in + +CPAdder(A1,A2,S,C,n) /\ RCAdder(A1,A2,S',C',n) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ1.in b/benchmarks/Regstab/bitvectors/comparisons/equ1.in new file mode 100644 index 0000000..f039b1f --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ1.in @@ -0,0 +1,78 @@ +% n >= 0 +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 68. +% +% % number of calls to fixpoint : 1 +% S_init : +% (7: [ T(v0) if n = v0 ]. +% 9: [ S1(v0) if n = v0 ]. +% 10: [ S2(v0) if n = v0 ]. +% 11: [ S3(v0) if n = v0 ]. +% ) +% S_loop : +% (42: [ S3(v0) if n = s(v0) ]. +% 51: [ S2(v0) if n = s(v0) ]. +% 36: [ S1(v0) if n = s(v0) ]. +% 50: [ T(v0) if n = s(v0) ]. +% ) +% The empty clauses : +% (39: [ n = 0 ]. +% 56: [ n = s(0) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=68. Generated=143. Kept=75. proofs=1. +% Usable=48. Sos=5. Demods=0. Limbo=0, Disabled=51. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=53. Back_subsumed=22. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=150. Nonunit_bsub_feature_tests=96. +% Megabytes=0.13. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== +set(prolog_style_variables). +assign(max_given, 100). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +clear(sat). +assign(order, kbo). + +set(random_loopdet). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +N(X) | T(X) . +T(0) . +N(X) | S1(X) . +N(X) | S2(X) . +N(X) | S3(X) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & (T(s(X)) <-> ((A(s(X)) <-> B(s(X))) & T(X) | -A(s(X)) & B(s(X)) )) ) . +S2(0) <-> $F . +S2(s(X)) <-> ( S2(X) | - (A(s(X)) <-> B(s(X))) ) . +S3(0) <-> $T. +S3(s(X)) <-> ( S3(X) & -B(s(X)) ) . + + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ1.stab b/benchmarks/Regstab/bitvectors/comparisons/equ1.stab new file mode 100644 index 0000000..81bb8a1 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ1.stab @@ -0,0 +1,15 @@ +// n >= 0 +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in +let Equal(Temp,X,Y,n) := /\i=1..n (X_i <-> Y_i) in +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in + +let Zero(X) := /\i=1..n ~X_i in + +LowerThan(T,A,B,n) /\ Zero(B) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ2.in b/benchmarks/Regstab/bitvectors/comparisons/equ2.in new file mode 100644 index 0000000..c755749 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ2.in @@ -0,0 +1,76 @@ +% Symmetry: n1 >= n2 /\ n2 >= n1 => n1 = n2 +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 114. +% +% % number of calls to fixpoint : 1 +% S_init : +% (8: [ T1(v0) if n = v0 ]. +% 10: [ S1(v0) if n = v0 ]. +% 11: [ T2(v0) if n = v0 ]. +% 13: [ S2(v0) if n = v0 ]. +% 14: [ S3(v0) if n = v0 ]. +% ) +% S_loop : +% (74: [ S3(v0) if n = s(v0) ]. +% 53: [ S2(v0) if n = s(v0) ]. +% 75: [ T2(v0) if n = s(v0) ]. +% 49: [ S1(v0) if n = s(v0) ]. +% 73: [ T1(v0) if n = s(v0) ]. +% ) +% The empty clauses : +% (57: [ n = 0 ]. +% 83: [ n = s(0) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=114. Generated=288. Kept=134. proofs=1. +% Usable=65. Sos=11. Demods=0. Limbo=0, Disabled=99. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=121. Back_subsumed=58. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=331. Nonunit_bsub_feature_tests=196. +% Megabytes=0.20. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 750). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +set(random_loopdet). +%set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +clear(sat). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( N(X) | T1(X) ) & T1(0) & ( N(X) | S1(X) ) ) & ( ( ( N(X) | T2(X) ) & T2(0) & ( N(X) | S2(X) ) ) ) & ( ( N(X) | S3(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & (T1(s(X)) <-> (((A(s(X)) <-> B(s(X))) & T1(X)) | (-A(s(X)) & B(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( T2(s(X)) <-> (((B(s(X)) <-> A(s(X))) & T2(X) ) | (-B(s(X)) & A(s(X))) ) )) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | - (A(s(X)) <-> B(s(X)) ) ) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ2.stab b/benchmarks/Regstab/bitvectors/comparisons/equ2.stab new file mode 100644 index 0000000..3971df9 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ2.stab @@ -0,0 +1,13 @@ +// Symmetry: n1 >= n2 /\ n2 >= n1 => n1 = n2 +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in + +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in + +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in + +LowerOrEqual(T1,A,B,n) /\ GreaterOrEqual(T2,A,B,n) /\ Different(T3,A,B,n) + +// vim:ft=regstab + diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ3.in b/benchmarks/Regstab/bitvectors/comparisons/equ3.in new file mode 100644 index 0000000..4b0e987 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ3.in @@ -0,0 +1,80 @@ +%Totality: n1 > n2 \/ n2 >= n1 +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 114. +% +% % number of calls to fixpoint : 1 +% S_init : +% (8: [ T1(v0) if n = v0 ]. +% 10: [ S1(v0) if n = v0 ]. +% 11: [ S2(v0) if n = v0 ]. +% 12: [ T2(v0) if n = v0 ]. +% 14: [ S3(v0) if n = v0 ]. +% ) +% S_loop : +% (53: [ S3(v0) if n = s(v0) ]. +% 75: [ T2(v0) if n = s(v0) ]. +% 74: [ S2(v0) if n = s(v0) ]. +% 49: [ S1(v0) if n = s(v0) ]. +% 73: [ T1(v0) if n = s(v0) ]. +% ) +% The empty clauses : +% (57: [ n = 0 ]. +% 83: [ n = s(0) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=114. Generated=288. Kept=134. proofs=1. +% Usable=65. Sos=11. Demods=0. Limbo=0, Disabled=99. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=121. Back_subsumed=58. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=331. Nonunit_bsub_feature_tests=196. +% Megabytes=0.20. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== +% + + + + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(random_loopdet). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( ( N(X) | T1(X) ) & T1(0) & ( N(X) | S1(X) ) ) & ( ( N(X) | S2(X) ) ) ) & ( ( ( N(X) | T2(X) ) & T2(0) & ( N(X) | S3(X) ) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & (T1(s(X)) <-> ( ( (A(s(X)) <-> B(s(X))) & T1(X) ) | (-A(s(X)) & B(s(X)) ) )) ) . + +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & (T2(s(X)) <-> ( ( (A(s(X)) <-> B(s(X))) & T2(X) ) | (A(s(X)) & -B(s(X)))) ) ) . + +S2(0) <-> $F . +S2(s(X)) <-> ( S2(X) | - (A(s(X)) <-> B(s(X))) ) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ3.stab b/benchmarks/Regstab/bitvectors/comparisons/equ3.stab new file mode 100644 index 0000000..f6be434 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ3.stab @@ -0,0 +1,17 @@ +// Totality: n1 > n2 \/ n2 >= n1 +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in + +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in + + +LowerThan(T1,A,B,n) /\ GreaterOrEqual(T2,A,B,n) + +// vim:ft=regstab + + +let Equal(Temp,X,Y,n) := /\i=1..n (X_i <-> Y_i) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ4.in b/benchmarks/Regstab/bitvectors/comparisons/equ4.in new file mode 100644 index 0000000..138a1f3 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ4.in @@ -0,0 +1,80 @@ +%Transitivity: n1 <= n2 /\ n2 <= n3 => n1 <= n3 +% ============================== PROOF ================================= +% +% % Proof 1 at 0.02 (+ 0.00) seconds. +% % Given clauses 214. +% +% % number of calls to fixpoint : 1 +% S_init : +% (10: [ L1(v0) if n = v0 ]. +% 12: [ S1(v0) if n = v0 ]. +% 13: [ L2(v0) if n = v0 ]. +% 15: [ S2(v0) if n = v0 ]. +% 16: [ L3(v0) if n = v0 ]. +% 18: [ S3(v0) if n = v0 ]. +% 19: [ S4(v0) if n = v0 ]. +% ) +% S_loop : +% (158: [ S4(v0) if n = s(v0) ]. +% 116: [ S3(v0) if n = s(v0) ]. +% 157: [ L3(v0) if n = s(v0) ]. +% 72: [ S2(v0) if n = s(v0) ]. +% 154: [ L2(v0) if n = s(v0) ]. +% 68: [ S1(v0) if n = s(v0) ]. +% 155: [ L1(v0) if n = s(v0) ]. +% ) +% The empty clauses : +% (120: [ n = 0 ]. +% 173: [ n = s(0) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=214. Generated=877. Kept=258. proofs=1. +% Usable=120. Sos=15. Demods=0. Limbo=0, Disabled=181. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=553. Back_subsumed=123. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=734. Nonunit_bsub_feature_tests=389. +% Megabytes=0.38. +% User_CPU=0.02, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 350). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(random_loopdet). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +%list(kbo_weights). +%s = 3. +%end_of_list. + +formulas(sos). +( ( N(X) | L1(X) ) & L1(0) & ( N(X) | S1(X) ) ) & ( ( N(X) | L2(X) ) & L2(0) & ( N(X) | S2(X) ) ) & ( ( ( ( N(X) | L3(X) ) & L3(0) & ( N(X) | S3(X) ) ) & ( ( N(X) | S4(X) ) ) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & (L1(s(X)) <-> ( ((A(s(X)) <-> B(s(X)) ) & L1(X)) | -A(s(X)) & B(s(X)) ) )) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & (L2(s(X)) <-> ( ((B(s(X)) <-> C(s(X)) ) & L2(X)) | -B(s(X)) & C(s(X)) ) )) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & (L3(s(X)) <-> ( ((A(s(X)) <-> C(s(X)) ) & L3(X)) | A(s(X)) & -C(s(X)) ) )) . +S4(0) <-> $F . +S4(s(X)) <-> ( S4(X) | - (A(s(X)) <-> C(s(X))) ) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ4.stab b/benchmarks/Regstab/bitvectors/comparisons/equ4.stab new file mode 100644 index 0000000..a373c4b --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ4.stab @@ -0,0 +1,11 @@ +// Transitivity: n1 <= n2 /\ n2 <= n3 => n1 <= n3 +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in + +LowerOrEqual(L1,A,B,n) /\ LowerOrEqual(L2,B,C,n) /\ GreaterThan(L3,A,C,n) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ5.in b/benchmarks/Regstab/bitvectors/comparisons/equ5.in new file mode 100644 index 0000000..fd68965 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ5.in @@ -0,0 +1,72 @@ +% 1 < 2 +============================== PROOF ================================= + +% Proof 1 at 0.01 (+ 0.00) seconds. +% Given clauses 123. + +% number of calls to fixpoint : 4 + S_init : + (59: [ S3(v0) if n = s(v0) ]. +) + S_loop : + (118: [ S3(v0) if n = s(s(v0)) ]. +) + The empty clauses : + (63: [ n = 0 ]. +79: [ n = s(0) ]. +117: [ n = s(s(0)) ]. +) max_rank 3 + +============================== end of proof ========================== + +============================== STATISTICS ============================ + +Given=123. Generated=366. Kept=157. proofs=1. +Usable=93. Sos=11. Demods=0. Limbo=0, Disabled=97. Hints=0. +Kept_by_rule=0, Deleted_by_rule=0. +Forward_subsumed=194. Back_subsumed=53. +Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +Demod_attempts=0. Demod_rewrites=0. +Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +Nonunit_fsub_feature_tests=282. Nonunit_bsub_feature_tests=197. +Megabytes=0.25. +User_CPU=0.01, System_CPU=0.00, Wall_clock=0. + +============================== end of statistics ===================== + + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 300). +set(raw). +set(index_flat). +set(print_gen). +set(superind). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( -A(s(0)) & $A$(s(0)) & ( N(X) | S1(X) ) ) & ( B(s(0)) & ( N(X) | S2(X) ) ) & ( ( ( N(X) | T(X) ) & T(0) & ( N(X) | S3(X) ) ) & ( ( N(X) | S4(X) ) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & -$A$$(s(X)) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & -$B$(s(X)) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & (T(s(X)) <-> ((A(s(X)) <-> B(s(X))) & T(X) | -A(s(X)) & B(s(X)))) ) . +S4(0) <-> $F . +S4(s(X)) <-> ( S4(X) | - (A(s(X)) <-> B(s(X))) ) . +A(s(X)) <-> $A$(X) . +$A$(s(X)) <-> $A$$(X) . +B(s(X)) <-> $B$(X) . +-T(s(0)). + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/comparisons/equ5.stab b/benchmarks/Regstab/bitvectors/comparisons/equ5.stab new file mode 100644 index 0000000..42da117 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/comparisons/equ5.stab @@ -0,0 +1,17 @@ +// Transitivity: 1 <= 2 +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in +let Equal(Temp,X,Y,n) := /\i=1..n (X_i <-> Y_i) in +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in + +let One(A) := A_1 /\ /\i=1..n ~A_i+1 in +let Two(A) := ~A_1 /\ A_2 /\ /\i=1..n ~A_i+2 in + +Two(A) /\ One(B) /\ LowerThan(T,A,B,n) | n>=2 + +// vim:ft=regstab + diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder1.stab b/benchmarks/Regstab/bitvectors/ripplecarry/adder1.stab new file mode 100644 index 0000000..7d3fd67 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder1.stab @@ -0,0 +1,8 @@ +// Prove that A+0=A with a ripple-carry adder +//expected: unsat +/\i=1..n ((S_i <-> (A_i (+) B_i (+) C_i)) /\ (C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i))) +/\ ~C_1 +/\ /\i=1..n ~B_i +/\ \/i=1..n (A_i (+) S_i) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder2.in b/benchmarks/Regstab/bitvectors/ripplecarry/adder2.in new file mode 100644 index 0000000..56075aa --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder2.in @@ -0,0 +1,70 @@ +% Theo: A + 0 = A +% ============================== PROOF ================================= +% % Cycle1 et Cycle2 +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 102. +% +% % number of calls to fixpoint : 4 +% S_init : +% (67: [ S3(v0) | $C$(v0) if n = s(v0) ]. +% 50: [ S2(v0) if n = s(v0) ]. +% 49: [ S1(v0) if n = s(v0) ]. +% ) +% S_loop : +% (91: [ S3(v0) | $C$(v0) if n = s(s(v0)) ]. +% 71: [ S2(v0) if n = s(s(v0)) ]. +% 69: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (52: [ n = 0 ]. +% 75: [ n = s(0) ]. +% 99: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=102. Generated=255. Kept=115. proofs=1. +% Usable=71. Sos=5. Demods=0. Limbo=0, Disabled=79. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=128. Back_subsumed=39. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=181. Nonunit_bsub_feature_tests=163. +% Megabytes=0.22. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. + +% ============================== end of statistics ===================== +%assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(random_loopdet). +clear(sat). +%assign(start_rank, 3). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). + + +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( ( N(X) | S2(X) ) ) & ( ( N(X) | S3(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A(s(X)) <-> B(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> (A(s(X)) & B(s(X)) | C(s(X)) & A(s(X)) | C(s(X)) & B(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & -B(s(X)) ) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | - (A(s(X)) <-> S(s(X))) ) . +C(s(X)) <-> $C$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder2.stab b/benchmarks/Regstab/bitvectors/ripplecarry/adder2.stab new file mode 100644 index 0000000..307ba16 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder2.stab @@ -0,0 +1,13 @@ +// Same as adder1.stab, except the syntax uses funtions +// A+0=A +//expected: unsat + +let Sum(i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder := /\i=1..n (Sum(i) /\ Carry(i)) /\ ~C_1 in +let NullB := /\i=1..n ~B_i in +let Conclusion := \/i=1..n (A_i (+) S_i) in + +Adder() /\ NullB() /\ Conclusion() + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder3.in b/benchmarks/Regstab/bitvectors/ripplecarry/adder3.in new file mode 100644 index 0000000..d082212 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder3.in @@ -0,0 +1,76 @@ +% Commutativity of the ripple-carry adder +% ============================== PROOF ================================= +% +% % Proof 1 at 0.02 (+ 0.00) seconds. +% % Given clauses 248. +% +% % number of calls to fixpoint : 6 +% S_init : +% (73: [ S1(v0) if n = s(s(v0)) ]. +% 74: [ S2(v0) if n = s(s(v0)) ]. +% 164: [ S3(v0) | -$CP$(v0) | -$C$(v0) if n = s(s(v0)) ]. +% 166: [ S3(v0) | $CP$(v0) | $C$(v0) if n = s(s(v0)) ]. +% ) +% S_loop : +% (302: [ S3(v0) | $CP$(v0) | $C$(v0) if n = s(s(s(v0))) ]. +% 300: [ S3(v0) | -$CP$(v0) | -$C$(v0) if n = s(s(s(v0))) ]. +% 169: [ S2(v0) if n = s(s(s(v0))) ]. +% 168: [ S1(v0) if n = s(s(s(v0))) ]. +% ) +% The empty clauses : +% (75: [ n = s(0) ]. +% 176: [ n = s(s(0)) ]. +% 312: [ n = s(s(s(0))) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=248. Generated=963. Kept=306. proofs=1. +% Usable=150. Sos=9. Demods=0. Limbo=0, Disabled=210. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=629. Back_subsumed=147. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=543. Nonunit_bsub_feature_tests=474. +% Megabytes=0.56. +% User_CPU=0.02, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== +% +% ============================== end of search ========================= + +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +%set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +clear(sat). +set(random_loopdet). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( N(s(X)) | S1(X) ) & -C(s(0)) ) & ( ( N(s(X)) | S2(X) ) & -CP(s(0)) ) & ( ( N(s(X)) | S3(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> (A1(s(X)) & A2(s(X)) | C(s(X)) & A1(s(X)) | C(s(X)) & A2(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( SP(s(X)) <-> -( - (A2(s(X)) <-> A1(s(X)) ) <-> CP(s(X))) ) & ( $CP$(s(X)) <-> (A2(s(X)) & A1(s(X)) | CP(s(X)) & A2(s(X)) | CP(s(X)) & A1(s(X))) ) ) ) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | - (S(s(X)) <-> SP(s(X))) ) . +C(s(X)) <-> $C$(X) . +CP(s(X)) <-> $CP$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder3.stab b/benchmarks/Regstab/bitvectors/ripplecarry/adder3.stab new file mode 100644 index 0000000..5c1b189 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder3.stab @@ -0,0 +1,11 @@ +// Commutativity of the ripple-carry adder +//expected: unsat + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in +let Different(X,Y) := \/i=1..n (X_i (+) Y_i) in + +Adder(A1,A2,S,C,n) /\ Adder(A2,A1,S',C',n) /\ Different(S,S') + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder4.in b/benchmarks/Regstab/bitvectors/ripplecarry/adder4.in new file mode 100644 index 0000000..3405071 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder4.in @@ -0,0 +1,96 @@ +% Associativity of the ripple-carry adder +% ============================== PROOF ================================= +% +% % Proof 1 at 1.73 (+ 0.07) seconds. +% % Given clauses 3734. +% +% % number of calls to fixpoint : 4 +% S_init : +% (130: [ S1(v0) if n = s(v0) ]. +% 135: [ S2(v0) if n = s(v0) ]. +% 136: [ S3(v0) if n = s(v0) ]. +% 137: [ S4(v0) if n = s(v0) ]. +% 790: [ S5(v0) | -$C2P$(v0) | -$C$(v0) | $C2$(v0) | $C1$(v0) if n = s(v0) ]. +% 792: [ S5(v0) | -$C2P$(v0) | $C$(v0) | $C2$(v0) | -$C1$(v0) if n = s(v0) ]. +% 793: [ S5(v0) | $C2P$(v0) | -$C$(v0) | -$C2$(v0) | $C1$(v0) if n = s(v0) ]. +% 795: [ S5(v0) | $C2P$(v0) | $C$(v0) | -$C2$(v0) | -$C1$(v0) if n = s(v0) ]. +% 797: [ S5(v0) | $C2P$(v0) | $C$(v0) | $C2$(v0) | $C1$(v0) if n = s(v0) ]. +% 789: [ S5(v0) | -$C2P$(v0) | -$C$(v0) | -$C2$(v0) | -$C1$(v0) if n = s(v0) ]. +% ) +% S_loop : +% (2700: [ S5(v0) | -$C2P$(v0) | -$C$(v0) | -$C2$(v0) | -$C1$(v0) if n = s(s(v0)) ]. +% 2703: [ S5(v0) | $C2P$(v0) | $C$(v0) | $C2$(v0) | $C1$(v0) if n = s(s(v0)) ]. +% 2701: [ S5(v0) | $C2P$(v0) | $C$(v0) | -$C2$(v0) | -$C1$(v0) if n = s(s(v0)) ]. +% 2699: [ S5(v0) | $C2P$(v0) | -$C$(v0) | -$C2$(v0) | $C1$(v0) if n = s(s(v0)) ]. +% 2698: [ S5(v0) | -$C2P$(v0) | $C$(v0) | $C2$(v0) | -$C1$(v0) if n = s(s(v0)) ]. +% 2697: [ S5(v0) | -$C2P$(v0) | -$C$(v0) | $C2$(v0) | $C1$(v0) if n = s(s(v0)) ]. +% 826: [ S4(v0) if n = s(s(v0)) ]. +% 813: [ S3(v0) if n = s(s(v0)) ]. +% 812: [ S2(v0) if n = s(s(v0)) ]. +% 811: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (142: [ n = 0 ]. +% 845: [ n = s(0) ]. +% 2747: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=3734. Generated=142527. Kept=4499. proofs=1. +% Usable=2213. Sos=40. Demods=0. Limbo=0, Disabled=2365. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=135844. Back_subsumed=2246. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=18371. Nonunit_bsub_feature_tests=6833. +% Megabytes=10.96. +% User_CPU=1.73, System_CPU=0.07, Wall_clock=2. +% +% ============================== end of statistics ===================== +% + +%assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 4000). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). + +set(rank_given). +set(random_loopdet). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +%list(kbo_weights). +%s = 3. +%end_of_list. + + +formulas(sos). +( ( N(X) | S1(X) ) & -C1(s(0)) ) & ( ( N(X) | S2(X) ) & -C(s(0)) ) & ( ( N(X) | S3(X) ) & -C2P(s(0)) ) & ( ( N(X) | S4(X) ) & -C2(s(0)) ) & ( ( N(X) | S5(X) ) ) . +S1(0) . +S1(s(X)) <-> ( S1(X) & ( ( B1(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C1(s(X))) ) & ( $C1$(s(X)) <-> ((A1(s(X)) & A2(s(X))) | (C1(s(X)) & A1(s(X)) ) | (C1(s(X)) & A2(s(X))) ) ) ) ) . +S2(0) . +S2(s(X)) <-> ( S2(X) & ( ( S(s(X)) <-> -( - (B1(s(X)) <-> A3(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> ((B1(s(X)) & A3(s(X))) | (C(s(X)) & B1(s(X))) | ( C(s(X)) & A3(s(X))) ) ) ) ) . +S3(0) . +S3(s(X)) <-> ( S3(X) & ( ( SP(s(X)) <-> -( - (A1(s(X)) <-> B2(s(X)) ) <-> C2P(s(X))) ) & ( $C2P$(s(X)) <-> (A1(s(X)) & B2(s(X)) | C2P(s(X)) & A1(s(X)) | C2P(s(X)) & B2(s(X))) ) ) ) . +S4(0) . +S4(s(X)) <-> ( S4(X) & ( ( B2(s(X)) <-> -( - (A2(s(X)) <-> A3(s(X)) ) <-> C2(s(X))) ) & ( $C2$(s(X)) <-> (A2(s(X)) & A3(s(X)) | C2(s(X)) & A2(s(X)) | C2(s(X)) & A3(s(X))) ) ) ) . +-S5(0) . +S5(s(X)) <-> ( S5(X) | - (S(s(X)) <-> SP(s(X))) ) . +C1(s(X)) <-> $C1$(X) . +C(s(X)) <-> $C$(X) . +C2P(s(X)) <-> $C2P$(X) . +C2(s(X)) <-> $C2$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder4.stab b/benchmarks/Regstab/bitvectors/ripplecarry/adder4.stab new file mode 100644 index 0000000..b84b23f --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder4.stab @@ -0,0 +1,13 @@ +// Associativity of the ripple-carry adder +//expected: unsat + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_2 in +let Different(X,Y) := \/i=1..n (X_i (+) Y_i) in + +Adder(A1,A2,B1,C1,n) /\ Adder(B1,A3,S,C1',n) +/\ Adder(A1,B2,S',C2',n) /\ Adder(A2,A3,B2,C2,n) +/\ Different(S,S') + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder5.in b/benchmarks/Regstab/bitvectors/ripplecarry/adder5.in new file mode 100644 index 0000000..2e04dc2 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder5.in @@ -0,0 +1,98 @@ +% 3+4=7 +% ============================== PROOF ================================= +% +% % Proof 1 at 1.06 (+ 0.07) seconds. +% % Given clauses 2572. +% +% % number of calls to fixpoint : 10 +% S_init : +% (646: [ S1(v0) if n = s(s(s(v0))) ]. +% 647: [ S2(v0) if n = s(s(s(v0))) ]. +% 648: [ S3(v0) if n = s(s(s(v0))) ]. +% 649: [ S4(v0) if n = s(s(s(v0))) ]. +% 2266: [ -$B$$(v0) | $A$$$(v0) | $SP$$$(v0) | -$SP$$(v0) | $B$$$(v0) | $A$$(v0) | -$SP$(v0) | S5(v0) | $C$(v0) | $B$(v0) | -$A$(v0) if n = s(s(s(v0))) ]. +% 2272: [ $B$$(v0) | $A$$$(v0) | $SP$$$(v0) | $SP$$(v0) | $B$$$(v0) | $A$$(v0) | -$SP$(v0) | S5(v0) | $C$(v0) | -$B$(v0) | $A$(v0) if n = s(s(s(v0))) ]. +% 2273: [ $B$$(v0) | $A$$$(v0) | $SP$$$(v0) | $SP$$(v0) | $B$$$(v0) | $A$$(v0) | $SP$(v0) | S5(v0) | $C$(v0) | $B$(v0) | $A$(v0) if n = s(s(s(v0))) ]. +% ) +% S_loop : +% (3433: [ $B$$(v0) | $A$$$(v0) | $SP$$$(v0) | $SP$$(v0) | $B$$$(v0) | $A$$(v0) | $SP$(v0) | S5(v0) | $C$(v0) | $B$(v0) | $A$(v0) if n = s(s(s(s(v0)))) ]. +% 3432: [ $B$$(v0) | $A$$$(v0) | $SP$$$(v0) | $SP$$(v0) | $B$$$(v0) | $A$$(v0) | -$SP$(v0) | S5(v0) | $C$(v0) | -$B$(v0) | $A$(v0) if n = s(s(s(s(v0)))) ]. +% 3426: [ -$B$$(v0) | $A$$$(v0) | $SP$$$(v0) | -$SP$$(v0) | $B$$$(v0) | $A$$(v0) | -$SP$(v0) | S5(v0) | $C$(v0) | $B$(v0) | -$A$(v0) if n = s(s(s(s(v0)))) ]. +% 2342: [ S4(v0) if n = s(s(s(s(v0)))) ]. +% 2341: [ S3(v0) if n = s(s(s(s(v0)))) ]. +% 2340: [ S2(v0) if n = s(s(s(s(v0)))) ]. +% 2339: [ S1(v0) if n = s(s(s(s(v0)))) ]. +% ) +% The empty clauses : +% (103: [ n = 0 ]. +% 192: [ n = s(0) ]. +% 698: [ n = s(s(0)) ]. +% 2407: [ n = s(s(s(0))) ]. +% 3438: [ n = s(s(s(s(0)))) ]. +% ) max_rank 4 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=2572. Generated=102397. Kept=3418. proofs=1. +% Usable=1905. Sos=33. Demods=0. Limbo=0, Disabled=1557. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=97107. Back_subsumed=1480. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=23473. Nonunit_bsub_feature_tests=5015. +% Megabytes=7.99. +% User_CPU=1.06, System_CPU=0.07, Wall_clock=1. +% +% ============================== end of statistics ===================== +% +% ============================== end of search ========================= + +set(prolog_style_variables). +assign(max_given, 6000). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +set(cycle2). +%set(random_loopdet). +%clear(sat). +%assign(start_rank, 3). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( A(s(0)) & $A$(s(0)) & -$A$$(s(0)) & ( N(X) | S2(X) ) ) & ( -B(s(0)) & -$B$(s(0)) & $B$$(s(0)) & ( N(X) | S3(X) ) ) & ( SP(s(0)) & $SP$(s(0)) & $SP$$(s(0)) & ( N(X) | S4(X) ) ) & ( ( N(X) | S5(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A(s(X)) <-> B(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> (A(s(X)) & B(s(X)) | C(s(X)) & A(s(X)) | C(s(X)) & B(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & -$A$$$(s(X)) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & -$B$$$(s(X)) ) . +S4(0) <-> $T . +S4(s(X)) <-> ( S4(X) & -$SP$$$(s(X)) ) . +S5(0) <-> $F . +S5(s(X)) <-> ( S5(X) | - (S(s(X)) <-> SP(s(X))) ) . +C(s(X)) <-> $C$(X) . +A(s(X)) <-> $A$(X) . +$A$(s(X)) <-> $A$$(X) . +$A$$(s(X)) <-> $A$$$(X) . +B(s(X)) <-> $B$(X) . +$B$(s(X)) <-> $B$$(X) . +$B$$(s(X)) <-> $B$$$(X) . +SP(s(X)) <-> $SP$(X) . +$SP$(s(X)) <-> $SP$$(X) . +$SP$$(s(X)) <-> $SP$$$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder5.stab b/benchmarks/Regstab/bitvectors/ripplecarry/adder5.stab new file mode 100644 index 0000000..efc1b07 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder5.stab @@ -0,0 +1,16 @@ +// 3+4=7 +//expected: unsat + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in +let Different(X,Y) := \/i=1..n (X_i (+) Y_i) in + +let Three(A) := A_1 /\ A_2 /\ ~A_3 /\ /\i=1..n ~A_i+3 in +let Four(A) := ~A_1 /\ ~A_2 /\ A_3 /\ /\i=1..n ~A_i+3 in +let Seven(A) := A_1 /\ A_2 /\ A_3 /\ /\i=1..n ~A_i+3 in + +Adder(A,B,S,C,n) /\ Three(A) /\ Four(B) /\ Seven(S') /\ Different(S,S') + +// vim:ft=regstab + diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder6.in b/benchmarks/Regstab/bitvectors/ripplecarry/adder6.in new file mode 100644 index 0000000..0c0e55a --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder6.in @@ -0,0 +1,77 @@ +% Unicity of the result +% ============================== PROOF ================================= +% +% % Proof 1 at 0.03 (+ 0.01) seconds. +% % Given clauses 386. +% +% % number of calls to fixpoint : 4 +% S_init : +% (81: [ S1(v0) if n = s(v0) ]. +% 82: [ S2(v0) if n = s(v0) ]. +% 174: [ S4(v0) | S3(v0) | $CP$(v0) | $C$(v0) if n = s(v0) ]. +% 176: [ S4(v0) | S3(v0) | -$CP$(v0) | -$C$(v0) if n = s(v0) ]. +% ) +% S_loop : +% (302: [ S4(v0) | S3(v0) | -$CP$(v0) | -$C$(v0) if n = s(s(v0)) ]. +% 304: [ S4(v0) | S3(v0) | $CP$(v0) | $C$(v0) if n = s(s(v0)) ]. +% 178: [ S2(v0) if n = s(s(v0)) ]. +% 177: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (88: [ n = 0 ]. +% 189: [ n = s(0) ]. +% 323: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=386. Generated=1885. Kept=444. proofs=1. +% Usable=217. Sos=12. Demods=0. Limbo=0, Disabled=284. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=1357. Back_subsumed=215. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=1433. Nonunit_bsub_feature_tests=699. +% Megabytes=0.80. +% User_CPU=0.03, System_CPU=0.01, Wall_clock=0. +% +% ============================== end of statistics ===================== +% +% ============================== end of search ========================= + +set(prolog_style_variables). +assign(max_given, 2900). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +set(random_loopdet). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | S1(X) ) & -C(s(0)) ) & ( ( N(X) | S2(X) ) & -CP(s(0)) ) & ( ( ( N(X) | S3(X) | S4(X) ) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( S(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> C(s(X))) ) & ( $C$(s(X)) <-> (A1(s(X)) & A2(s(X)) | C(s(X)) & A1(s(X)) | C(s(X)) & A2(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & ( ( SP(s(X)) <-> -( - (A1(s(X)) <-> A2(s(X)) ) <-> CP(s(X))) ) & ( $CP$(s(X)) <-> (A1(s(X)) & A2(s(X)) | CP(s(X)) & A1(s(X)) | CP(s(X)) & A2(s(X))) ) ) ) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | - (S(s(X)) <-> SP(s(X))) ) . +S4(0) <-> $F . +S4(s(X)) <-> ( S4(X) | - (C(s(X)) <-> CP(s(X))) ) . +C(s(X)) <-> $C$(X) . +CP(s(X)) <-> $CP$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/adder6.stab b/benchmarks/Regstab/bitvectors/ripplecarry/adder6.stab new file mode 100644 index 0000000..3ae9cc6 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/adder6.stab @@ -0,0 +1,11 @@ +// Unicity of the result +//expected: unsat + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in +let Different(X,Y) := \/i=1..n (X_i (+) Y_i) in + +Adder(A1,A2,S,C,n) /\ Adder(A1,A2,S',C',n) /\ (Different(S,S') \/ Different(C,C')) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/cex.stab b/benchmarks/Regstab/bitvectors/ripplecarry/cex.stab new file mode 100644 index 0000000..525e079 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/cex.stab @@ -0,0 +1,12 @@ +// Associativity of the ripple-carry adder +//expected: sat + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in +let Different(X,Y) := \/i=1..n (X_i (+) Y_i) in + +Adder(A1,A2,B1,C1,n) /\ Adder(B1,A3,S,C1',n) +/\ Adder(A1,B2,S',C2',n) /\ Adder(A2,A3,B2,C2,n) + +// vim:ft=regstab diff --git a/benchmarks/Regstab/bitvectors/ripplecarry/refutation.xml b/benchmarks/Regstab/bitvectors/ripplecarry/refutation.xml new file mode 100644 index 0000000..e05d303 --- /dev/null +++ b/benchmarks/Regstab/bitvectors/ripplecarry/refutation.xml @@ -0,0 +1,189044 @@ + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))] /\ ~C_1 /\ A_1 /\ A_2 /\ ~A_3 /\ /\i=1..n [~A_i+3] /\ ~B_1 /\ ~B_2 /\ B_3 /\ /\i=1..n [~B_i+3] /\ S'_1 /\ S'_2 /\ S'_3 /\ /\i=1..n [~S'_i+3] /\ \/i=1..n [S_i (+) S'_i], |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi1) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi6) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi11) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi16) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi21) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi26) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi35) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi40) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi49) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi54) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi63) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi68) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +C_1, ~C_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi77) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi78) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi79) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi80) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +C_1, ~C_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi81) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi82) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi83) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi84) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi85) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi90) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi91) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi92) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi93) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi94) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi95) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi96) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi97) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi98) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi99) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi100) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi101) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi102) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi103) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi104) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi105) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +C_1, ~C_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi106) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi107) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi108) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi109) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi110) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi111) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi112) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi113) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi114) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi115) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi116) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi117) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi118) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi123) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi132) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi133) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi134) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi135) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi136) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi137) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi138) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi139) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi140) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi141) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi142) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi143) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi144) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi162) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi213) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi214) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi215) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi216) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi217) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi218) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi219) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi220) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi221) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi226) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi227) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi228) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi229) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi230) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi231) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi232) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi233) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi234) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi235) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi236) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi237) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi238) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi239) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi240) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi241) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi242) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi243) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi244) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi245) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi246) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi247) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi248) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi249) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi250) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi251) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi252) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi253) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi254) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi259) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi268) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi269) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi270) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi271) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi272) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi273) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi274) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi275) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi276) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi277) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi278) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi279) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi280) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi301) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +--> (Phi358) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +--> (Phi379) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi436) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi457) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi514) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi566) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi1 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi2) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi3) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi4) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi5) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi6 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi7) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi8) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi9) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi10) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi11 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi12) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi13) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi14) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi15) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi16 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi17) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi18) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi19) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi20) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi21 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi22) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi23) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi24) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi25) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi26 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi27) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi28) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi29) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi30) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi31) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi32) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi33) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi34) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi35 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi36) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi37) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi38) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi39) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi40 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi41) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi42) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi43) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi44) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi45) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi46) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi47) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi48) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi49 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi50) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi51) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi52) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi53) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi54 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi55) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi56) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi57) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi58) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi59) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi60) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi61) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi62) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi63 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi64) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi65) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi66) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi67) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi68 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi69) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi70) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi71) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi72) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi73) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi74) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi75) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi76) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi77 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi78 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi79 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi80 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi81 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi82 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi83 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi84 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi85 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi86) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi87) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi88) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi89) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi90 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi91 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi92 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi93 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi94 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi95 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi96 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi97 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi98 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi99 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi100 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi101 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi102 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi103 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi104 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi105 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi106 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi107 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi108 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi109 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi110 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi111 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi112 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi113 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi114 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi115 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi116 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi117 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi118 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi119) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi120) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi121) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi122) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi123 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi124) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi125) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi126) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi127) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi128) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi129) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi130) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi131) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi132 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi133 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi134 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi135 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi136 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi137 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi138 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi139 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi140 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi141 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi142 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi143 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi144 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi145) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi146) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi147) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi148) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi149) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi150) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi151) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi152) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi153) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi158) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi159) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi160) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi161) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi162 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi163) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi164) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi165) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi166) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi167) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi168) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi169) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi170) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi171) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi172) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi173) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi174) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi175) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi176) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi177) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi178) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi179) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi180) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi181) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi182) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi183) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi184) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi185) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi186) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi187) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi192) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi201) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi202) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi203) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi204) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi205) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi206) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi207) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi208) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi209) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi210) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi211) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi212) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi213 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi214 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi215 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi216 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi217 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi218 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +C_1, ~C_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi219 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi220 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi221 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi222) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi223) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi224) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi225) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi226 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi227 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi228 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi229 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi230 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi231 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi232 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi233 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi234 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi235 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi236 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi237 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi238 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi239 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi240 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi241 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi242 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi243 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +C_1, ~C_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi244 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi245 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi246 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi247 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi248 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +C_1, ~C_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi249 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi250 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi251 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi252 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi253 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi254 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi255) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi256) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi257) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi258) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi259 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi260) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi261) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi262) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi263) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi264) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi265) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi266) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi267) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi268 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi269 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi270 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi271 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi272 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi273 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi274 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi275 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi276 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi277 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi278 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi279 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi280 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi281) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi286) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi291) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi296) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi301 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi302) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi307) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi316) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi321) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi330) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi335) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi344) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi349) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi358 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi359) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi364) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi369) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi374) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi379 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi380) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi385) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +--> (Phi394) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +--> (Phi399) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi408) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi413) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi422) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi427) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi436 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi437) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi442) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi447) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi452) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi457 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi458) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi463) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi472) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi477) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi486) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi491) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi500) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi505) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + + +Phi514 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi515) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi520) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi525) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi530) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi532) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi537) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi539) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi541) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi543) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi555) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi560) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi562) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi564) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi566 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi567) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi568) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi569) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi570) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi571) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi572) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi573) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi574) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi575) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi576) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi577) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi578) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi579) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi580) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi581) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi582) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi583) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi584) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi585) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi586) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi587) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi588) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi589) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi590) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi591) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi596) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi605) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi606) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi607) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi608) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi609) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi610) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi611) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi612) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi613) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi614) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi615) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi616) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi2 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi3 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi4 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi5 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi7 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi8 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi9 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi10 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi12 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi13 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi14 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_3, ~A_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi15 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi17 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi18 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi19 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi20 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi22 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi23 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi24 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi25 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi27 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi28 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi29 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi30 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi31 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi32 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi33 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi34 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi36 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi37 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi38 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi39 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi41 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi42 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi43 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi44 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi45 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi46 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi47 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi48 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi50 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi51 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi52 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi53 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi55 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi56 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi57 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi58 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi59 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi60 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi61 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi62 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi64 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi65 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi66 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi67 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi69 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi70 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi71 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi72 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi73 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi74 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi75 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi76 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi86 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi87 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi88 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi89 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi119 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi120 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi121 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi122 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi124 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi125 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi126 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi127 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi128 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi129 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi130 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi131 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi145 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi146 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi147 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi148 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi149 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi150 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi151 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi152 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi153 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi154) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi155) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi156) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi157) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi158 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi159 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi160 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi161 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi163 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi164 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi165 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi166 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi167 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi168 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi169 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi170 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi171 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi172 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi173 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi174 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi175 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi176 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +A_3, ~A_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi177 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi178 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi179 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi180 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi181 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +A_3, ~A_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi182 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi183 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi184 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi185 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi186 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi187 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi188) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi189) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi190) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi191) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi192 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi193) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi194) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi195) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi196) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi197) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi198) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi199) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi200) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi201 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi202 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi203 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi204 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi205 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi206 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi207 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi208 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi209 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi210 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi211 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi212 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi222 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi223 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi224 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi225 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi255 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi256 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi257 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi258 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi260 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi261 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi262 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi263 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi264 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi265 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi266 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi267 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi281 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi282) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi283) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi284) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi285) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi286 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi287) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi288) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi289) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi290) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi291 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi292) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi293) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi294) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi295) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi296 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi297) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi298) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi299) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi300) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi302 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi303) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi304) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi305) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi306) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi307 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi308) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi309) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi310) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi311) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi312) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi313) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi314) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi315) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi316 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi317) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi318) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi319) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi320) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi321 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi322) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi323) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi324) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +--> (Phi325) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi326) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi327) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi328) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi329) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi330 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi331) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi332) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi333) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi334) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi335 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi336) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi337) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi338) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi339) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi340) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi341) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi342) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi343) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + + +Phi344 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi345) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi346) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi347) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi348) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi349 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi350) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi351) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi352) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi353) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi354) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi355) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi356) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi357) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi359 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi360) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi361) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi362) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi363) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi364 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi365) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +--> (Phi366) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi367) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi368) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi369 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi370) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi371) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi372) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi373) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi374 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi375) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi376) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi377) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi378) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi380 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi381) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi382) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi383) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi384) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi385 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi386) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi387) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi388) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi389) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi390) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi391) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi392) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi393) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi394 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi395) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +--> (Phi396) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi397) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi398) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi399 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi400) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +--> (Phi401) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +--> (Phi402) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +--> (Phi403) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi404) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +--> (Phi405) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi406) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +--> (Phi407) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi408 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi409) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi410) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi411) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi412) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi413 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi414) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi415) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi416) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi417) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi418) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi419) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi420) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi421) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + + +Phi422 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi423) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi424) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi425) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi426) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi427 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi428) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +--> (Phi429) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi430) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi431) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi432) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi433) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi434) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi435) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi437 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi438) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi439) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi440) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi441) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi442 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi443) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi444) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi445) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi446) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi447 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi448) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi449) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi450) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi451) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi452 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi453) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi454) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi455) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi456) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi458 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi459) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi460) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi461) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi462) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi463 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi464) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi465) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi466) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi467) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi468) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi469) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi470) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi471) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi472 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi473) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi474) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi475) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi476) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi477 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi478) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi479) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi480) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi481) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi482) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi483) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi484) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi485) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi486 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi487) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi488) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi489) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi490) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi491 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi492) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi493) + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi494) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi495) + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi496) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi497) + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi498) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi499) + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi500 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi501) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi502) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi503) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi504) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi505 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi506) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +--> (Phi507) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi508) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi509) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi510) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi511) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi512) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi513) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi515 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi516) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi517) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi518) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi519) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi520 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi521) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +--> (Phi522) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +--> (Phi523) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi524) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi525 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi526) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi527) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi528) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi529) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi530 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi531) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi532 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi533) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi534) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi535) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi536) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi537 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi538) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi539 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi540) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi541 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi542) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi543 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi544) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi549) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi551) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi553) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi555 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi556) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +--> (Phi557) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +--> (Phi558) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +--> (Phi559) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi560 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +C_1, ~C_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi561) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi562 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi563) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi564 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi565) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi567 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi568 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi569 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi570 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi571 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi572 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi573 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi574 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi575 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi576 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi577 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi578 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi579 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi580 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi581 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi582 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi583 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi584 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi585 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi586 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi587 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi588 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi589 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi590 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi591 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi592) + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi593) + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi594) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi595) + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi596 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi597) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +--> (Phi598) + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi599) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi600) + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi601) + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi602) + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi603) + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +--> (Phi604) + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi605 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi606 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi607 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi608 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi609 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi610 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + + +Phi611 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi612 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi613 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi614 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi615 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi616 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi154 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi155 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi156 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi157 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi188 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi189 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi190 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi191 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi193 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi194 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi195 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi196 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi197 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi198 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi199 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi200 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi282 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi283 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi284 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi285 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi287 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi288 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi289 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi290 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi292 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi293 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi294 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi295 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi297 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi298 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi299 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi300 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi303 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi304 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi305 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi306 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi308 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi309 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi310 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi311 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi312 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi313 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi314 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi315 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi317 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi318 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi319 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi320 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi322 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi323 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi324 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi325 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi326 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi327 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi328 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi329 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi331 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi332 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi333 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi334 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi336 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi337 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi338 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi339 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi340 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi341 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi342 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi343 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi345 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi346 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi347 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi348 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi350 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi351 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi352 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi353 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi354 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi355 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi356 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi357 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+4, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi360 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi361 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi362 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi363 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi365 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi366 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi367 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi368 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi370 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi371 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi372 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi373 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi375 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + + + + + + + + + + + +Phi376 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi377 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi378 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+4, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4, S'_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi381 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi382 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi383 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi384 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi386 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi387 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi388 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi389 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi390 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi391 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + + +Phi392 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi393 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi395 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi396 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi397 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi398 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi400 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi401 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi402 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + +Phi403 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, n >= 0 |- + + + + + + + + + + + + + + + +Phi404 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi405 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + + +Phi406 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi407 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi409 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi410 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi411 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi412 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi414 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi415 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi416 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi417 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi418 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi419 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi420 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi421 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi423 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi424 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi425 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi426 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi428 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + +Phi429 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, n >= 0 |- + + + + + + + + + + + + + + + +Phi430 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi431 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi432 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi433 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi434 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi435 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi438 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi439 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi440 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi441 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi443 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi444 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi445 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi446 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi448 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi449 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi450 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi451 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi453 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi454 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi455 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi456 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi459 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi460 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi461 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi462 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi464 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi465 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi466 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi467 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi468 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi469 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi470 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi471 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi473 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi474 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi475 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi476 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi478 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi479 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi480 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi481 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi482 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi483 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi484 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi485 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi487 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi488 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi489 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi490 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi492 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi493 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi494 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi495 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi496 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi497 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi498 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi499 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi501 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi502 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi503 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi504 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi506 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi507 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi508 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_3, ~B_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi509 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi510 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi511 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi512 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi513 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi516 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi517 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi518 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi519 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi521 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi522 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+3, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi523 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +A_2, ~A_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi524 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi526 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi527 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi528 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_3, ~A_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi529 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_1, ~A_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi531 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi533 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi534 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi535 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi536 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi538 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~C_1, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi540 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi542 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi544 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi545) + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi546) + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +--> (Phi547) + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +--> (Phi548) + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi549 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +A_3, ~A_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, B_n+1, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi550) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi551 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi552) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi553 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_3, ~S'_3 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +--> (Phi554) + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi556 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi557 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi558 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + + + + + + + + + + + +Phi559 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi561 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi563 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi565 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +~B_n+4, B_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi592 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi593 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi594 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi595 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_2, ~S'_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+3, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+3, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi597 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + +Phi598 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + + + + + + + + + + + + + + + +Phi599 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi600 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi601 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +S'_1, ~S'_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S'_n+2, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+2, ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi602 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, A_1, A_n+1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi603 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_n+2, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi604 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~B_n+4, ~A_n+1, ~A_3, ~A_n+3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, A_1, A_2, A_n+2, C_n+1, C_n+2, n >= 0 |- + +n <= 0, empty disjunction |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, ~C_n+1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+1, ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + +~S_n+1, S_n+1 |- + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +~B_n+1, B_n+1 |- + + + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +(S_n+1 (+) S'_n+1) \/ \/i=1..n [S_i (+) S'_i], ~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1 (+) S'_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +S_n+1, ~S_n+1 |- + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_n+1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], \/i=1..n [S_i (+) S'_i], ~S'_n+4, ~S_n+1, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_1, S'_2, S'_3, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi545 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi546 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi547 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, ~C_n+1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+2, ~C_n+2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1) /\ (~C_n+1 \/ ~B_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (~A_n+1 \/ ~B_n+1) /\ (~C_n+1 \/ ~A_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +B_n+1, ~B_n+1 |- + + + +C_n+1, ~C_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +C_n+1, ~C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +B_n+1, ~B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), ~A_n+1 \/ ~B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, S_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +B_n+1, ~B_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +A_n+1, ~A_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+1, ~A_3, ~C_1, ~C_n+1, ~C_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + + + + + + + + + + + +Phi548 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_n+1, ~B_2, ~B_n+4, ~A_n+1, ~A_3, ~A_n+4, ~C_1, ~C_n+2, S'_3, S_n+1, B_n+2, B_3, B_n+3, A_1, A_2, A_n+2, A_n+3, C_n+1, n >= 0 |- + +B_2, ~B_2 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, S_n+1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+2, ~A_n+1, ~A_n+2, ~A_3, ~C_1, B_n+1, B_3, B_n+3, B_n+4, A_1, A_2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi550 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~B_n+3, ~A_n+1, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi552 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+3, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + + +Phi554 + +/\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], /\i=1..n [~A_i+3], /\i=1..n [~B_i+3], /\i=1..n [~S'_i+3], ~S'_n+4, ~B_1, ~B_2, ~B_n+4, ~A_n+2, ~A_3, ~A_n+4, ~C_1, S'_3, S_n+1, B_n+1, B_n+2, B_3, B_n+3, A_1, A_n+1, A_2, A_n+3, C_n+1, C_n+2, n >= 0 |- + +B_1, ~B_1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1)) /\ (C_n+2 <-< ((A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1)) /\ /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), (A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1) \/ C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1 \/ C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), A_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~A_n+1, A_n+1 |- + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, ~C_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ A_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_n+1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~A_n+1, A_n+1 |- + + + +~C_n+1, C_n+1 |- + + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], S_n+1 <-< ((A_n+1 (+) B_n+1) (+) C_n+1), C_n+1 /\ B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) (+) C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~C_n+1, C_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 <-< B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, S_n+1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_n+1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + +~B_n+1, B_n+1 |- + + + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], (A_n+1 (+) B_n+1) <-< C_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], A_n+1 (+) B_n+1, /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~B_n+1, B_n+1 |- + + +~S'_n+4 /\ /\i=1..n [~S'_i+3], ~B_n+4 /\ /\i=1..n [~B_i+3], ~A_n+4 /\ /\i=1..n [~A_i+3], /\i=1..n [(S_i <-< ((A_i (+) B_i) (+) C_i)) /\ (C_i+1 <-< ((A_i /\ B_i \/ C_i /\ A_i) \/ C_i /\ B_i))], ~S_n+1, ~B_1, ~B_2, ~A_n+1, ~A_3, ~A_n+3, ~C_1, B_n+1, B_n+2, B_3, B_n+3, B_n+4, A_1, A_2, A_n+2, A_n+4, C_n+1, C_n+2, n >= 0 |- + +~A_n+4, A_n+4 |- + + + + +~C_n+1, C_n+1 |- + + + + + +~C_n+2, C_n+2 |- + + + + + + \ No newline at end of file diff --git a/benchmarks/Regstab/ceres/ex1.in b/benchmarks/Regstab/ceres/ex1.in new file mode 100644 index 0000000..7914849 --- /dev/null +++ b/benchmarks/Regstab/ceres/ex1.in @@ -0,0 +1,69 @@ +% + % ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 53. +% +% % number of calls to fixpoint : 4 +% S_init : +% (22: [ S1(v0) if n = s(v0) ]. +% 28: [ Cl1psi(v0) if n = s(v0) ]. +% 33: [ -$A$(v0) if n = s(v0) ]. +% ) +% S_loop : +% (44: [ -$A$(v0) if n = s(s(v0)) ]. +% 39: [ Cl1psi(v0) if n = s(s(v0)) ]. +% 35: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (21: [ n = 0 ]. +% 38: [ n = s(0) ]. +% 49: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=53. Generated=92. Kept=57. proofs=1. +% Usable=34. Sos=4. Demods=0. Limbo=0, Disabled=35. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=14. Back_subsumed=19. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=60. Nonunit_bsub_feature_tests=77. +% Megabytes=0.11. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== +% + + +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +set(print_gen). +set(superind). +set(rank_given). +set(cycle2). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( N(X) | Cl0phi(X) ) & (-Cl0phi(0) & (-Cl1psi(0) | A(s(0)) ) ) & ( N(X) | S1(X) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( (-Cl0phi(s(X)) | Cl1psi(s(X))) & (-Cl0phi(s(X)) | -$A$(s(X))) & (-Cl1psi(s(X)) | Cl1psi(X)) & (-Cl1psi(s(X)) | -A(s(X)) | $A$(s(X))) ) ) . +A(s(X)) <-> $A$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/ceres/ex1.stab b/benchmarks/Regstab/ceres/ex1.stab new file mode 100644 index 0000000..00bbb32 --- /dev/null +++ b/benchmarks/Regstab/ceres/ex1.stab @@ -0,0 +1,13 @@ +// Example 1 coming from Ceres, simplified +//expected: unsat + +let CS0 := ~Cl0phi_0 /\ (~Cl1psi_0 \/ A_1) in +let CS1(k) := + (~Cl0phi_k+1 \/ Cl1psi_k+1) /\ + (~Cl0phi_k+1 \/ ~A_k+2) /\ + (~Cl1psi_k+1 \/ Cl1psi_k) /\ + (~Cl1psi_k+1 \/ ~A_k+1 \/ A_k+2) + in + +Cl0phi_n /\ CS0() /\ /\k=0..n CS1(k) | n>=0 + diff --git a/benchmarks/Regstab/ceres/ex1original.in b/benchmarks/Regstab/ceres/ex1original.in new file mode 100644 index 0000000..71db2e9 --- /dev/null +++ b/benchmarks/Regstab/ceres/ex1original.in @@ -0,0 +1,67 @@ +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 77. +% +% % number of calls to fixpoint : 4 +% S_init : +% (37: [ S1(v0) if n = s(v0) ]. +% 43: [ Cl1psi(v0) if n = s(v0) ]. +% 48: [ -$A$(v0) if n = s(v0) ]. +% ) +% S_loop : +% (65: [ -$A$(v0) if n = s(s(v0)) ]. +% 57: [ Cl1psi(v0) if n = s(s(v0)) ]. +% 51: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (30: [ n = 0 ]. +% 56: [ n = s(0) ]. +% 73: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=77. Generated=153. Kept=86. proofs=1. +% Usable=49. Sos=6. Demods=0. Limbo=0, Disabled=55. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=21. Back_subsumed=31. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=87. Nonunit_bsub_feature_tests=125. +% Megabytes=0.15. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== + +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). + +set(superind). +set(cycle1). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( N(X) | Cl0phi(X) ) & -Cl0phi(0) & (-Cl1phi(0) | A(s(0))) & (-Cl1psi(0) | A(s(0))) & (-Cl1psi(0) | A(0) ) & ( N(X) | S1(s(X)) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( (-Cl0phi(s(X)) | Cl1psi(s(X))) & (-Cl0phi(s(X)) | -$A$(s(X))) & (-$Cl1phi$(s(X)) | Cl1psi(s(X))) & (-Cl1psi(s(X)) | Cl1phi(X)) & (-Cl1psi(s(X)) | Cl1psi(X)) & (-Cl1psi(s(X)) | -A(s(X)) | $A$(s(X))) ) ) . +A(s(X)) <-> $A$(X) . +Cl1phi(s(X)) <-> $Cl1phi$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/ceres/ex1original.stab b/benchmarks/Regstab/ceres/ex1original.stab new file mode 100644 index 0000000..586ffea --- /dev/null +++ b/benchmarks/Regstab/ceres/ex1original.stab @@ -0,0 +1,15 @@ +// Example 1 coming from Ceres +//expected: unsat + +let CS0 := ~Cl0phi_0 /\ (~Cl1phi_0 \/ A_1) /\ (~Cl1psi_0 \/ A_1) /\ (~Cl1psi_0 \/ A_0) in +let CS1(k) := + (~Cl0phi_k+1 \/ Cl1psi_k+1) /\ + (~Cl0phi_k+1 \/ ~A_k+2) /\ + (~Cl1phi_k+2 \/ Cl1psi_k+1) /\ + (~Cl1psi_k+1 \/ Cl1phi_k) /\ + (~Cl1psi_k+1 \/ Cl1psi_k) /\ + (~Cl1psi_k+1 \/ ~A_k+1 \/ A_k+2) + in + +Cl0phi_n /\ CS0() /\ /\k=0..n CS1(k) | n>=0 + diff --git a/benchmarks/Regstab/ceres/ex2.in b/benchmarks/Regstab/ceres/ex2.in new file mode 100644 index 0000000..90adcd2 --- /dev/null +++ b/benchmarks/Regstab/ceres/ex2.in @@ -0,0 +1,67 @@ +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 137. +% +% % number of calls to fixpoint : 4 +% S_init : +% (62: [ S1(v0) if n = s(v0) ]. +% 70: [ Cl1Phi(v0) if n = s(v0) ]. +% 85: [ Cl2chi(v0) | Cl0chi(v0) if n = s(v0) ]. +% ) +% S_loop : +% (113: [ Cl2chi(v0) | Cl0chi(v0) if n = s(s(v0)) ]. +% 99: [ Cl1Phi(v0) if n = s(s(v0)) ]. +% 89: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (67: [ n = 0 ]. +% 112: [ n = s(0) ]. +% 140: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=137. Generated=325. Kept=164. proofs=1. +% Usable=90. Sos=7. Demods=0. Limbo=0, Disabled=104. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=80. Back_subsumed=67. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=346. Nonunit_bsub_feature_tests=312. +% Megabytes=0.26. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== +% + +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( N(X) | Cl0phi(X) ) & (-Cl0phi(0) | Cl1Phi(0)) & (-Cl0phi(0) | Cl0chi(s(0)) | A(s(0)) ) & (-Cl0phi(0) | -A(0) ) & (-Cl1Phi(0) | A(0) ) & -Cl0chi(0) & (-Cl2chi(0) | -A(0) ) & ( N(X) | S1(s(X)) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( (-Cl0phi(s(X)) | Cl1Phi(s(X))) & (-Cl0phi(s(X)) | Cl0chi(s(X)) | $A$(s(X))) & (-Cl0phi(s(X)) | $Cl2chi$(s(X))) & (-Cl1Phi(s(X)) | Cl1Phi(X)) & (-Cl1Phi(s(X)) | A(s(X))) & (-Cl2chi(s(X)) | -A(s(X)) | Cl2chi(X)) & (-Cl0chi(s(X)) | Cl0chi(X)) ) ) . +A(s(X)) <-> $A$(X) . +Cl2chi(s(X)) <-> $Cl2chi$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/ceres/ex2.stab b/benchmarks/Regstab/ceres/ex2.stab new file mode 100644 index 0000000..1a9c2aa --- /dev/null +++ b/benchmarks/Regstab/ceres/ex2.stab @@ -0,0 +1,22 @@ +// Example 2 coming from Ceres, simplified +//expected: unsat + +let CS0 := + (~Cl0phi_0 \/ Cl1Phi_0) /\ + (~Cl0phi_0 \/ Cl0chi_1 \/ A_1) /\ + (~Cl0phi_0 \/ ~A_0) /\ + (~Cl1Phi_0 \/ A_0) /\ + ~Cl0chi_0 /\ + (~Cl2chi_0 \/ ~A_0) +in +let CS1(k) := + (~Cl0phi_k+1 \/ Cl1Phi_k+1) /\ + (~Cl0phi_k+1 \/ Cl0chi_k+1 \/ A_k+2) /\ + (~Cl0phi_k+1 \/ Cl2chi_k+2) /\ + (~Cl1Phi_k+1 \/ Cl1Phi_k) /\ + (~Cl1Phi_k+1 \/ A_k+1) /\ + (~Cl2chi_k+1 \/ ~A_k+1 \/ Cl2chi_k) /\ + (~Cl0chi_k+1 \/ Cl0chi_k) +in + +Cl0phi_n /\ CS0() /\ /\k=0..n CS1(k) | n>=0 diff --git a/benchmarks/Regstab/ceres/ex2original.stab b/benchmarks/Regstab/ceres/ex2original.stab new file mode 100644 index 0000000..5276495 --- /dev/null +++ b/benchmarks/Regstab/ceres/ex2original.stab @@ -0,0 +1,24 @@ +// Example 2 coming from Ceres +//expected: unsat + +let CS0 := + (Cl0phi_0 -> Cl1psi_0) /\ + (Cl0phi_0 -> Cl2chi_0) /\ + (Cl1Phi_0 -> A_0) /\ + (Cl1psi_0 -> Cl1Phi_0) /\ + (Cl1psi_0 -> (Cl0chi_1 \/ A_1)) /\ + ~Cl0chi_0 /\ + (~Cl2chi_0 \/ ~A_0) +in +let CS1(k) := + (Cl0phi_k+1 -> Cl1psi_k+1) /\ + (Cl0phi_k+1 -> Cl2chi_k+2) /\ + (Cl1Phi_k+1 -> Cl1Phi_k) /\ + (Cl1Phi_k+1 -> A_k+1) /\ + (Cl1psi_k+1 -> Cl1Phi_k+1) /\ + (Cl1psi_k+1 -> (Cl0chi_k+1 \/ A_k+2)) /\ + (Cl2chi_k+1 /\ A_k+1 -> Cl2chi_k) /\ + (Cl0chi_k+1 -> Cl0chi_k) +in + +Cl0phi_n /\ CS0() /\ /\k=0..n CS1(k) | n>=0 diff --git a/benchmarks/Regstab/presburger/arith1.in b/benchmarks/Regstab/presburger/arith1.in new file mode 100644 index 0000000..0de1f47 --- /dev/null +++ b/benchmarks/Regstab/presburger/arith1.in @@ -0,0 +1,88 @@ +% n + p > n +% ============================== PROOF ================================= +% +% % Proof 1 at 0.43 (+ 0.02) seconds. +% % Given clauses 1207. +% +% % number of calls to fixpoint : 4 +% S_init : +% (976: [ S1(v0) if n = s(v0) ]. +% 984: [ S2(v0) if n = s(v0) ]. +% 1630: [ -$T1$(v0) if n = s(v0) ]. +% 1631: [ S3(v0) if n = s(v0) ]. +% 1632: [ T2(v0) if n = s(v0) ]. +% ) +% S_loop : +% (2020: [ T2(v0) if n = s(s(v0)) ]. +% 2021: [ S3(v0) if n = s(s(v0)) ]. +% 2018: [ -$T1$(v0) if n = s(s(v0)) ]. +% 1725: [ S2(v0) if n = s(s(v0)) ]. +% 1717: [ S1(v0) if n = s(s(v0)) ]. +% ) +% The empty clauses : +% (1461: [ n = 0 ]. +% 1735: [ n = s(0) ]. +% 2128: [ n = s(s(0)) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ + +% Given=1207. Generated=31818. Kept=2491. proofs=1. +% Usable=670. Sos=55. Demods=0. Limbo=0, Disabled=1848. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=29084. Back_subsumed=1766. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=38395. Nonunit_bsub_feature_tests=4408. +% Megabytes=3.21. +% User_CPU=0.43, System_CPU=0.02, Wall_clock=1. +% +% ============================== end of statistics ===================== + +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(random_loopdet). +set(rank_given). +set(binary_resolution). +set(ordered_res). +clear(sat). +set(random_loopdet). +set(back_subsume). +assign(order, kbo). +%assign(literal_selection, all_negative). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +( ( N(X) | -$M$$(X) ) & ( N(X) | -$P$$(X) ) ) & ( ( N(X) | -$M$(X) ) & ( N(X) | -$P$(X) ) & ( N(X) | ($MplusP$$(X) <-> $T1$$(X) ) ) & ( N(X) | $S1$(X) ) & -T1(s(0)) ) & ( ( ( N(X) | $T2$(X) ) & T2(0) & ( N(X) | $S2$(X) ) ) & ( ( N(X) | $S3$(X) ) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & ( ( MplusP(s(X)) <-> -( - (M(s(X)) <-> P(s(X)) ) <-> T1(s(X))) ) & ( $T1$(s(X)) <-> (M(s(X)) & P(s(X)) | T1(s(X)) & M(s(X)) | T1(s(X)) & P(s(X))) ) ) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & (T2(s(X)) <-> ((MplusP(s(X)) <-> M(s(X))) & T2(X) | -MplusP(s(X)) & M(s(X)))) ) . +S3(0) <-> $F . +S3(s(X)) <-> ( S3(X) | - (MplusP(s(X)) <-> M(s(X))) ) . +T1(s(X)) <-> $T1$(X) . +$M$(s(X)) <-> $M$$(X) . +M(s(X)) <-> $M$(X) . +P(s(X)) <-> $P$(X) . +$P$(s(X)) <-> $P$$(X) . +MplusP(s(X)) <-> $MplusP$(X) . +$MplusP$(s(X)) <-> $MplusP$$(X) . +T1(s(X)) <-> $T1$(X) . +$T1$(s(X)) <-> $T1$$(X) . +S1(s(X)) <-> $S1$(X). +T2(s(X)) <-> $T2$(X). +S2(s(X)) <-> $S2$(X). +S3(s(X)) <-> $S3$(X). +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/presburger/arith1.stab b/benchmarks/Regstab/presburger/arith1.stab new file mode 100644 index 0000000..d610958 --- /dev/null +++ b/benchmarks/Regstab/presburger/arith1.stab @@ -0,0 +1,31 @@ +// n+p >= n +// +// WARNING: we have to take care of possible overflowing carries! +// -> thus we consider (n+1)-bit vectors +// -> we must state explicitly that the last bit of n and p is null +// (of course this is not the case for n+p) +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in +let Equal(Temp,X,Y,n) := /\i=1..n (X_i <-> Y_i) in +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := ~A_n+1 /\ ~B_n+1 /\ (S_n+1 <-> C_n+1) /\ /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in + +let Zero(A) := /\i=1..n ~A_i in +let One(A) := A_1 /\ /\i=1..n ~A_i+1 in +let Two(A) := ~A_1 /\ A_2 /\ /\i=1..n ~A_i+2 in +let Three(A) := A_1 /\ A_2 /\ /\i=1..n ~A_i+2 in +let Four(A) := ~A_1 /\ ~A_2 /\ A_3 /\ /\i=1..n ~A_i+3 in +let Five(A) := A_1 /\ ~A_2 /\ A_3 /\ /\i=1..n ~A_i+3 in + +let LastBitNull := ~N_n+1 /\ ~P_n+1 in + +LastBitNull() /\ Adder(N,P,NplusP,T1,n+1) /\ LowerThan(T2,NplusP,N,n+1) | n>=0 + +// vim:ft=regstab diff --git a/benchmarks/Regstab/presburger/arith2.in b/benchmarks/Regstab/presburger/arith2.in new file mode 100644 index 0000000..85eafc9 --- /dev/null +++ b/benchmarks/Regstab/presburger/arith2.in @@ -0,0 +1,64 @@ +%assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 20000). +set(raw). +%set(index_flat). +%set(print_gen). +assign(max_literals, 8). +assign(max_depth, 4). +set(superind). +%set(cycle2). +set(rank_given). +%clear(sat). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | -$M1$(X) ) & ( N(X) | -$M2$(X) ) & ( N(X) | -$M3$(X) ) & ( N(X) | -$P$(X) ) ) & ( ( N(X) | $T1$(X) ) & T1(0) & ( N(X) | $S1$(X) ) ) & ( ( N(X) | $T2$(X) ) & T2(0) & ( N(X) | $S2$(X) ) ) & ( ( N(X) | $S3$(X) ) & -T3(s(0)) ) & ( ( N(X) | $S4$(X) ) & -T4(s(0)) ) & ( ( N(X) | $S5$(X) ) & -T5(s(0)) ) . +N(X) | ( ($T6$(X) & T6(0) & $S6$(X) & $S7$(X) ) | ( $T7$(X) & T7(0) & $S8$(X) & $S9$(X) ) ). +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & (T1(s(X)) <-> ((M1(s(X)) <-> M2(s(X))) & T1(X) | -M1(s(X)) & M2(s(X)))) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & (T2(s(X)) <-> ((M2(s(X)) <-> M3(s(X))) & T2(X) | -M2(s(X)) & M3(s(X)))) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & ( ( M1plusP(s(X)) <-> -( - (M1(s(X)) <-> P(s(X)) ) <-> T3(s(X))) ) & ( $T3$(s(X)) <-> (M1(s(X)) & P(s(X)) | T3(s(X)) & M1(s(X)) | T3(s(X)) & P(s(X))) ) ) ) . +S4(0) <-> $T . +S4(s(X)) <-> ( S4(X) & ( ( M2plusP(s(X)) <-> -( - (M2(s(X)) <-> P(s(X)) ) <-> T4(s(X))) ) & ( $T4$(s(X)) <-> (M2(s(X)) & P(s(X)) | T4(s(X)) & M2(s(X)) | T4(s(X)) & P(s(X))) ) ) ) . +S5(0) <-> $T . +S5(s(X)) <-> ( S5(X) & ( ( M3plusP(s(X)) <-> -( - (M3(s(X)) <-> P(s(X)) ) <-> T5(s(X))) ) & ( $T5$(s(X)) <-> (M3(s(X)) & P(s(X)) | T5(s(X)) & M3(s(X)) | T5(s(X)) & P(s(X))) ) ) ) . +S6(0) <-> $T . +S6(s(X)) <-> ( S6(X) & (T6(s(X)) <-> ((M1plusP(s(X)) <-> M2plusP(s(X))) & T6(X) | -M1plusP(s(X)) & M2plusP(s(X)))) ) . +S7(0) <-> $F . +S7(s(X)) <-> ( S7(X) | - (M1plusP(s(X)) <-> M2plusP(s(X))) ) . +S8(0) <-> $T . +S8(s(X)) <-> ( S8(X) & (T7(s(X)) <-> ((M2plusP(s(X)) <-> M3plusP(s(X))) & T7(X) | -M2plusP(s(X)) & M3plusP(s(X)))) ) . +S9(0) <-> $F . +S9(s(X)) <-> ( S9(X) | - (M2plusP(s(X)) <-> M3plusP(s(X))) ) . +T3(s(X)) <-> $T3$(X) . +T4(s(X)) <-> $T4$(X) . +T5(s(X)) <-> $T5$(X) . +T6(s(X)) <-> $T6$(X) . +T7(s(X)) <-> $T7$(X) . +M1(s(X)) <-> $M1$(X) . +M2(s(X)) <-> $M2$(X) . +M3(s(X)) <-> $M3$(X) . +P(s(X)) <-> $P$(X) . +T1(s(X)) <-> $T1$(X) . +T2(s(X)) <-> $T2$(X) . +S1(s(X)) <-> $S1$(X) . +S2(s(X)) <-> $S2$(X) . +S3(s(X)) <-> $S3$(X) . +S4(s(X)) <-> $S4$(X) . +S5(s(X)) <-> $S5$(X) . + +S6(s(X)) <-> $S6$(X) . +S7(s(X)) <-> $S7$(X) . +S8(s(X)) <-> $S8$(X) . +S9(s(X)) <-> $S9$(X) . +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/presburger/arith2.stab b/benchmarks/Regstab/presburger/arith2.stab new file mode 100644 index 0000000..55e069c --- /dev/null +++ b/benchmarks/Regstab/presburger/arith2.stab @@ -0,0 +1,28 @@ +// n1 <= n2 <= n3 => n1 + p <= n2 + p <= n3 + p +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in +let Equal(Temp,X,Y,n) := /\i=1..n (X_i <-> Y_i) in +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n ( Sum(A,B,S,C,i) /\ Carry(A,B,C,i) ) /\ ~C_1 in + + +let LastBitNull() := ~N1_n+1 /\ ~N2_n+1 /\ ~N3_n+1 /\ ~P_n+1 in + +LastBitNull() +/\ LowerOrEqual(T1,N1,N2,n+1) +/\ LowerOrEqual(T2,N2,N3,n+1) +/\ Adder(N1,P,N1plusP,T3,n+1) +/\ Adder(N2,P,N2plusP,T4,n+1) +/\ Adder(N3,P,N3plusP,T5,n+1) +/\ (GreaterThan(T6,N1plusP,N2plusP,n+1) \/ GreaterThan(T7,N2plusP,N3plusP,n+1)) +| n>=0 + +// vim:ft=regstab + diff --git a/benchmarks/Regstab/presburger/arith2bis.in b/benchmarks/Regstab/presburger/arith2bis.in new file mode 100644 index 0000000..ae70b45 --- /dev/null +++ b/benchmarks/Regstab/presburger/arith2bis.in @@ -0,0 +1,64 @@ +%assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 20000). +set(raw). +%set(index_flat). +%set(print_gen). +%assign(max_literals, 8). +%assign(max_depth, 4). +set(superind). +%set(cycle2). +set(rank_given). +%clear(sat). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | -$M1$(X) ) & ( N(X) | -$M2$(X) ) & ( N(X) | -$M3$(X) ) & ( N(X) | -$P$(X) ) ) & ( ( N(X) | $T1$(X) ) & T1(0) & ( N(X) | $S1$(X) ) ) & ( ( N(X) | $T2$(X) ) & T2(0) & ( N(X) | $S2$(X) ) ) & ( ( N(X) | $S3$(X) ) & -T3(s(0)) ) & ( ( N(X) | $S4$(X) ) & -T4(s(0)) ) & ( ( N(X) | $S5$(X) ) & -T5(s(0)) ) . +N(X) | ( ($T6$(X) & T6(0) & $S6$(X) & $S7$(X) ) | ( $T7$(X) & T7(0) & $S8$(X) & $S9$(X) ) ). +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & (T1(s(X)) <-> ((M1(s(X)) <-> M2(s(X))) & T1(X) | -M1(s(X)) & M2(s(X)))) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & (T2(s(X)) <-> ((M2(s(X)) <-> M3(s(X))) & T2(X) | -M2(s(X)) & M3(s(X)))) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & ( ( M1plusP(s(X)) <-> -( - (M1(s(X)) <-> P(s(X)) ) <-> T3(s(X))) ) & ( $T3$(s(X)) <-> (M1(s(X)) & P(s(X)) | T3(s(X)) & M1(s(X)) | T3(s(X)) & P(s(X))) ) ) ) . +S4(0) <-> $T . +S4(s(X)) <-> ( S4(X) & ( ( M2plusP(s(X)) <-> -( - (M2(s(X)) <-> P(s(X)) ) <-> T4(s(X))) ) & ( $T4$(s(X)) <-> (M2(s(X)) & P(s(X)) | T4(s(X)) & M2(s(X)) | T4(s(X)) & P(s(X))) ) ) ) . +S5(0) <-> $T . +S5(s(X)) <-> ( S5(X) & ( ( M3plusP(s(X)) <-> -( - (M3(s(X)) <-> P(s(X)) ) <-> T5(s(X))) ) & ( $T5$(s(X)) <-> (M3(s(X)) & P(s(X)) | T5(s(X)) & M3(s(X)) | T5(s(X)) & P(s(X))) ) ) ) . +S6(0) <-> $T . +S6(s(X)) <-> ( S6(X) & (T6(s(X)) <-> ((M1plusP(s(X)) <-> M2plusP(s(X))) & T6(X) | -M1plusP(s(X)) & M2plusP(s(X)))) ) . +S7(0) <-> $F . +S7(s(X)) <-> ( S7(X) | - (M1plusP(s(X)) <-> M2plusP(s(X))) ) . +S8(0) <-> $T . +S8(s(X)) <-> ( S8(X) & (T7(s(X)) <-> ((M2plusP(s(X)) <-> M3plusP(s(X))) & T7(X) | -M2plusP(s(X)) & M3plusP(s(X)))) ) . +S9(0) <-> $F . +S9(s(X)) <-> ( S9(X) | - (M2plusP(s(X)) <-> M3plusP(s(X))) ) . +T3(s(X)) <-> $T3$(X) . +T4(s(X)) <-> $T4$(X) . +T5(s(X)) <-> $T5$(X) . +T6(s(X)) <-> $T6$(X) . +T7(s(X)) <-> $T7$(X) . +M1(s(X)) <-> $M1$(X) . +M2(s(X)) <-> $M2$(X) . +M3(s(X)) <-> $M3$(X) . +P(s(X)) <-> $P$(X) . +T1(s(X)) <-> $T1$(X) . +T2(s(X)) <-> $T2$(X) . +S1(s(X)) <-> $S1$(X) . +S2(s(X)) <-> $S2$(X) . +S3(s(X)) <-> $S3$(X) . +S4(s(X)) <-> $S4$(X) . +S5(s(X)) <-> $S5$(X) . + +S6(s(X)) <-> $S6$(X) . +S7(s(X)) <-> $S7$(X) . +S8(s(X)) <-> $S8$(X) . +S9(s(X)) <-> $S9$(X) . +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/presburger/arith3.in b/benchmarks/Regstab/presburger/arith3.in new file mode 100644 index 0000000..954967a --- /dev/null +++ b/benchmarks/Regstab/presburger/arith3.in @@ -0,0 +1,41 @@ +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 3500). +%set(raw). +set(binary_resolution). +assign(order, kbo). +predicate_order([ N,S3, S4, M1, M2, P1, $M1$, $M2$, $M3$,P2, M1plusP1, M2plusP2, S1, S5, T5, T6, T8, $T5$, $T6$, S2, $P1$, $P2$, $P3$, M3, P3,T1, T3, S6 ]). +assign(age_part, 1). +assign(max_depth, 4). +assign(max_megs, 2000). +set(back_subsume). +set(back_demod). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | -$M1$(X) ) & ( N(X) | -$M2$(X) ) & ( N(X) | -$M3$(X) ) & ( N(X) | -$P1$(X) ) & ( N(X) | -$P2$(X) ) & ( N(X) | -$P3$(X) ) ) & ( ( N(X) | T1(X) ) & T1(0) & ( N(X) | S1(s(X)) ) ) & ( ( N(X) | T3(X) ) & T3(0) & ( N(X) | S2(s(X)) ) ) & ( ( N(X) | S3(s(X)) ) & -T5(s(0)) ) & ( ( N(X) | S4(s(X)) ) & -T6(s(0)) ) & ( ( ( ( N(X) | T8(X) ) & T8(0) & ( N(X) | S5(s(X)) ) ) & ( ( N(X) | S6(s(X)) ) ) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & (T1(s(X)) <-> ((M1(s(X)) <-> M2(s(X))) & T1(X) | -M1(s(X)) & M2(s(X)))) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & (T3(s(X)) <-> ((P1(s(X)) <-> P2(s(X))) & T3(X) | -P1(s(X)) & P2(s(X)))) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & ( ( M1plusP1(s(X)) <-> -( - (M1(s(X)) <-> P1(s(X)) ) <-> T5(s(X))) ) & ( $T5$(s(X)) <-> (M1(s(X)) & P1(s(X)) | T5(s(X)) & M1(s(X)) | T5(s(X)) & P1(s(X))) ) ) ) . +S4(0) <-> $T . +S4(s(X)) <-> ( S4(X) & ( ( M2plusP2(s(X)) <-> -( - (M2(s(X)) <-> P2(s(X)) ) <-> T6(s(X))) ) & ( $T6$(s(X)) <-> (M2(s(X)) & P2(s(X)) | T6(s(X)) & M2(s(X)) | T6(s(X)) & P2(s(X))) ) ) ) . +S5(0) <-> $T . +S5(s(X)) <-> ( S5(X) & (T8(s(X)) <-> ((M1plusP1(s(X)) <-> M2plusP2(s(X))) & T8(X) | -M1plusP1(s(X)) & M2plusP2(s(X)))) ) . +S6(0) <-> $F . +S6(s(X)) <-> ( S6(X) | - (M1plusP1(s(X)) <-> M2plusP2(s(X))) ) . +T5(s(X)) <-> $T5$(X) . +T6(s(X)) <-> $T6$(X) . +M1(s(X)) <-> $M1$(X) . +M2(s(X)) <-> $M2$(X) . +M3(s(X)) <-> $M3$(X) . +P1(s(X)) <-> $P1$(X) . +P2(s(X)) <-> $P2$(X) . +P3(s(X)) <-> $P3$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/presburger/arith3.stab b/benchmarks/Regstab/presburger/arith3.stab new file mode 100644 index 0000000..5261ac8 --- /dev/null +++ b/benchmarks/Regstab/presburger/arith3.stab @@ -0,0 +1,34 @@ +// n1 <= n2 /\ p1 <= p2 ==> n1 + p1 <= n2 + p2 +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in +let Equal(Temp,X,Y,n) := /\i=1..n (X_i <-> Y_i) in +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in + +let Zero(A) := /\i=1..n ~A_i in +let One(A) := A_1 /\ /\i=1..n ~A_i+1 in +let Two(A) := ~A_1 /\ A_2 /\ /\i=1..n ~A_i+2 in +let Three(A) := A_1 /\ A_2 /\ /\i=1..n ~A_i+2 in +let Four(A) := ~A_1 /\ ~A_2 /\ A_3 /\ /\i=1..n ~A_i+3 in +let Five(A) := A_1 /\ ~A_2 /\ A_3 /\ /\i=1..n ~A_i+3 in + +let LastBitNull := ~N1_n+1 /\ ~N2_n+1 /\ ~N3_n+1 /\ ~P1_n+1 /\ ~P2_n+1 /\ ~P3_n+1 in + +LastBitNull() +/\ LowerOrEqual(T1,N1,N2,n+1) +/\ LowerOrEqual(T3,P1,P2,n+1) +/\ Adder(N1,P1,N1plusP1,T5,n+1) +/\ Adder(N2,P2,N2plusP2,T6,n+1) +/\ GreaterThan(T8,N1plusP1,N2plusP2,n+1) +| n>=0 + +// vim:ft=regstab + + diff --git a/benchmarks/Regstab/presburger/arith4.in b/benchmarks/Regstab/presburger/arith4.in new file mode 100644 index 0000000..d157367 --- /dev/null +++ b/benchmarks/Regstab/presburger/arith4.in @@ -0,0 +1,73 @@ +set(prolog_style_variables). +assign(max_given, 2000). +set(raw). +set(index_flat). +%set(print_gen). +assign(max_literals, 7). +set(superind). +%set(cycle2). +clear(sat). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | -$M1$(X) ) & ( N(X) | -$M2$(X) ) & ( N(X) | -$M3$(X) ) & ( N(X) | -$P1$(X) ) & ( N(X) | -$P2$(X) ) & ( N(X) | -$P3$(X) ) ) & ( ( N(X) | $T1$(X) ) & T1(0) & ( N(X) | $S1$(X) ) ) & ( ( N(X) | $T2$(X) ) & T2(0) & ( N(X) | $S2$(X) ) ) & ( ( N(X) | $T3$(X) ) & T3(0) & ( N(X) | $S3$(X) ) ) & ( ( N(X) | $T4$(X) ) & T4(0) & ( N(X) | $S4$(X) ) ) & ( ( N(X) | $S5$(X) ) & -T5(s(0)) ) & ( ( N(X) | $S6$(X) ) & -T6(s(0)) ) & ( ( N(X) | $S7$(X) ) & -T7(s(0)) ) & (N(X) | ( $T8$(X) & T8(0) & $S8$(X) & $S9$(X) ) | ( $T9$(X) & T9(0) & $S11$(X) & $S12$(X) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & (T1(s(X)) <-> ((M1(s(X)) <-> M2(s(X))) & T1(X) | -M1(s(X)) & M2(s(X)))) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & (T2(s(X)) <-> ((M2(s(X)) <-> M3(s(X))) & T2(X) | -M2(s(X)) & M3(s(X)))) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & (T3(s(X)) <-> ((P1(s(X)) <-> P2(s(X))) & T3(X) | -P1(s(X)) & P2(s(X)))) ) . +S4(0) <-> $T . +S4(s(X)) <-> ( S4(X) & (T4(s(X)) <-> ((P2(s(X)) <-> P3(s(X))) & T4(X) | -P2(s(X)) & P3(s(X)))) ) . +S5(0) <-> $T . +S5(s(X)) <-> ( S5(X) & ( ( M1plusP1(s(X)) <-> -( - (M1(s(X)) <-> P1(s(X)) ) <-> T5(s(X))) ) & ( $T5$(s(X)) <-> (M1(s(X)) & P1(s(X)) | T5(s(X)) & M1(s(X)) | T5(s(X)) & P1(s(X))) ) ) ) . +S6(0) <-> $T . +S6(s(X)) <-> ( S6(X) & ( ( M2plusP2(s(X)) <-> -( - (M2(s(X)) <-> P2(s(X)) ) <-> T6(s(X))) ) & ( $T6$(s(X)) <-> (M2(s(X)) & P2(s(X)) | T6(s(X)) & M2(s(X)) | T6(s(X)) & P2(s(X))) ) ) ) . +S7(0) <-> $T . +S7(s(X)) <-> ( S7(X) & ( ( M3plusP3(s(X)) <-> -( - (M3(s(X)) <-> P3(s(X)) ) <-> T7(s(X))) ) & ( $T7$(s(X)) <-> (M3(s(X)) & P3(s(X)) | T7(s(X)) & M3(s(X)) | T7(s(X)) & P3(s(X))) ) ) ) . +S8(0) <-> $T . +S8(s(X)) <-> ( S8(X) & (T8(s(X)) <-> ((M1plusP1(s(X)) <-> M2plusP2(s(X))) & T8(X) | -M1plusP1(s(X)) & M2plusP2(s(X)))) ) . +S9(0) <-> $F . +S9(s(X)) <-> ( S9(X) | - (M1plusP1(s(X)) <-> M2plusP2(s(X))) ) . +S11(0) <-> $T . +S11(s(X)) <-> ( S11(X) & (T9(s(X)) <-> ((M2plusP2(s(X)) <-> M3plusP3(s(X))) & T9(X) | -M2plusP2(s(X)) & M3plusP3(s(X)))) ) . +S12(0) <-> $F . +S12(s(X)) <-> ( S12(X) | - (M2plusP2(s(X)) <-> M3plusP3(s(X))) ) . +T5(s(X)) <-> $T5$(X) . +T6(s(X)) <-> $T6$(X) . +T7(s(X)) <-> $T7$(X) . +M1(s(X)) <-> $M1$(X) . +M2(s(X)) <-> $M2$(X) . +M3(s(X)) <-> $M3$(X) . +P1(s(X)) <-> $P1$(X) . +P2(s(X)) <-> $P2$(X) . +P3(s(X)) <-> $P3$(X) . + +T1(s(X)) <-> $T1$(X) . +T2(s(X)) <-> $T2$(X) . +T3(s(X)) <-> $T2$(X) . +T4(s(X)) <-> $T2$(X) . +S1(s(X)) <-> $S1$(X) . +S2(s(X)) <-> $S2$(X) . +S3(s(X)) <-> $S3$(X) . +S4(s(X)) <-> $S4$(X) . +S5(s(X)) <-> $S5$(X) . + +S6(s(X)) <-> $S6$(X) . +S7(s(X)) <-> $S7$(X) . +S8(s(X)) <-> $S8$(X) . +S9(s(X)) <-> $S9$(X) . + + +S11(s(X)) <-> $S11$(X) . +S12(s(X)) <-> $S12$(X) . + +end_of_list. \ No newline at end of file diff --git a/benchmarks/Regstab/presburger/arith4.stab b/benchmarks/Regstab/presburger/arith4.stab new file mode 100644 index 0000000..fa82ae5 --- /dev/null +++ b/benchmarks/Regstab/presburger/arith4.stab @@ -0,0 +1,32 @@ +// n1 <= n2 <= n3 /\ p1 <= p2 <= p3 ==> n1 + p1 <= n2 + p2 <= n3 + p3 +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in +let Equal(Temp,X,Y,n) := /\i=1..n (X_i <-> Y_i) in +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in + + +let LastBitNull := ~N1_n+1 /\ ~N2_n+1 /\ ~N3_n+1 /\ ~P1_n+1 /\ ~P2_n+1 /\ ~P3_n+1 in + +LastBitNull() +/\ LowerOrEqual(T1,N1,N2,n+1) +/\ LowerOrEqual(T2,N2,N3,n+1) +/\ LowerOrEqual(T3,P1,P2,n+1) +/\ LowerOrEqual(T4,P2,P3,n+1) +/\ Adder(N1,P1,N1plusP1,T5,n+1) +/\ Adder(N2,P2,N2plusP2,T6,n+1) +/\ Adder(N3,P3,N3plusP3,T7,n+1) +/\ (GreaterThan(T8,N1plusP1,N2plusP2,n+1) \/ GreaterThan(T9,N2plusP2,N3plusP3,n+1)) +| n>=0 + +// vim:ft=regstab + + + diff --git a/benchmarks/Regstab/presburger/arith5.in b/benchmarks/Regstab/presburger/arith5.in new file mode 100644 index 0000000..b947ed8 --- /dev/null +++ b/benchmarks/Regstab/presburger/arith5.in @@ -0,0 +1,67 @@ +set(prolog_style_variables). +assign(max_given, 14000). +%set(raw). +set(index_flat). +set(print_gen). +set(superind). +%set(cycle2). +%set(random_loopdet). +set(rank_given). +%set(random_given). +set(binary_resolution). +set(ordered_res). +%clear(sat). +set(random_loopdet). +%set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | -$Q$(X) ) & ( N(X) | -$R$(X) ) ) & ( M1(s(0)) & ( N(X) | $S1$(X) ) ) & ( M2(s(0)) & -$M2$(s(0)) & $M2$$(s(0)) & ( N(X) | $S2$(X) ) ) & ( M3(s(0)) & $M3$(s(0)) & ( N(X) | $S3$(X) ) ) & ( -M4(s(0)) & -$M4$(s(0)) & $M4$$(s(0)) & ( N(X) | $S4$(X) ) ) & ( ( N(X) | $S5$(X) ) & -T1(s(0)) ) & ( ( N(X) | $T2$(X) ) & T2(0) & ( N(X) | $S6$(X) ) ) & ( ( N(X) | $T3$(X) ) & T3(0) & ( N(X) | $S7$(X) ) ) & ( ( ( N(X) | $T4$(X) ) & T4(0) & ( N(X) | $S8$(X) ) ) ) & ( ( ( N(X) | $T5$(X) ) & T5(0) & ( N(X) | $S9$(X) ) ) ) . +S1(0) <-> $T . +S1(s(X)) <-> ( S1(X) & -$M1$(s(X)) ) . +S2(0) <-> $T . +S2(s(X)) <-> ( S2(X) & -$M2$$$(s(X)) ) . +S3(0) <-> $T . +S3(s(X)) <-> ( S3(X) & -$M3$$(s(X)) ) . +S4(0) <-> $T . +S4(s(X)) <-> ( S4(X) & -$M4$$$(s(X)) ) . +S5(0) <-> $T . +S5(s(X)) <-> ( S5(X) & ( ( QpR(s(X)) <-> -( - (Q(s(X)) <-> R(s(X)) ) <-> T1(s(X))) ) & ( $T1$(s(X)) <-> (Q(s(X)) & R(s(X)) | T1(s(X)) & Q(s(X)) | T1(s(X)) & R(s(X))) ) ) ) . +S6(0) <-> $T . +S6(s(X)) <-> ( S6(X) & (T2(s(X)) <-> ((M1(s(X)) <-> QpR(s(X))) & T2(X) | -M1(s(X)) & QpR(s(X)))) ) . +S7(0) <-> $T . +S7(s(X)) <-> ( S7(X) & (T3(s(X)) <-> ((QpR(s(X)) <-> M2(s(X))) & T3(X) | -QpR(s(X)) & M2(s(X)))) ) . +S8(0) <-> $T . +S8(s(X)) <-> ( S8(X) & (T4(s(X)) <-> ((Q(s(X)) <-> M3(s(X))) & T4(X) | -Q(s(X)) & M3(s(X)))) ) . +S9(0) <-> $T . +S9(s(X)) <-> ( S9(X) & (T5(s(X)) <-> ((R(s(X)) <-> M4(s(X))) & T5(X) | -R(s(X)) & M4(s(X)))) ) . +M1(s(X)) <-> $M1$(X) . +M2(s(X)) <-> $M2$(X) . +$M2$(s(X)) <-> $M2$$(X) . +$M2$$(s(X)) <-> $M2$$$(X) . +M3(s(X)) <-> $M3$(X) . +$M3$(s(X)) <-> $M3$$(X) . +M4(s(X)) <-> $M4$(X) . +$M4$(s(X)) <-> $M4$$(X) . +$M4$$(s(X)) <-> $M4$$$(X) . +T1(s(X)) <-> $T1$(X) . +Q(s(X)) <-> $Q$(X) . +R(s(X)) <-> $R$(X) . +S1(s(X)) <-> $S1$(X) . +S2(s(X)) <-> $S2$(X) . +S3(s(X)) <-> $S3$(X) . +S4(s(X)) <-> $S4$(X) . +S5(s(X)) <-> $S5$(X) . +S6(s(X)) <-> $S6$(X) . +S7(s(X)) <-> $S7$(X) . +S8(s(X)) <-> $S8$(X) . +S9(s(X)) <-> $S9$(X) . +T2(s(X)) <-> $T2$(X) . +T3(s(X)) <-> $T3$(X) . +T4(s(X)) <-> $T4$(X) . +T5(s(X)) <-> $T5$(X) . +end_of_list. + diff --git a/benchmarks/Regstab/presburger/arith5.stab b/benchmarks/Regstab/presburger/arith5.stab new file mode 100644 index 0000000..14aa12f --- /dev/null +++ b/benchmarks/Regstab/presburger/arith5.stab @@ -0,0 +1,35 @@ +// 1 <= x+y <= 5 /\ x >= 3 /\ y >= 4 +//expected: unsat + +let LowerOrEqual(Temp,X,Y,n) := Temp_n /\ Temp_0 /\ /\i=1..n (Temp_i <-> ((X_i <-> Y_i) /\ Temp_i-1 \/ ~X_i /\ Y_i)) in +let Equal(Temp,X,Y,n) := /\i=1..n (X_i <-> Y_i) in +let Different(Temp,X,Y,n) := \/i=1..n (X_i (+) Y_i) in +let LowerThan(Temp,X,Y,n) := LowerOrEqual(Temp,X,Y,n) /\ Different(Temp,X,Y,n) in +let GreaterOrEqual(Temp,X,Y,n) := LowerOrEqual(Temp,Y,X,n) in +let GreaterThan(Temp,X,Y,n) := LowerThan(Temp,Y,X,n) in + +let Sum(A,B,S,C,i) := S_i <-> (A_i (+) B_i (+) C_i) in +let Carry(A,B,C,i) := C_i+1 <-> (A_i /\ B_i \/ C_i /\ A_i \/ C_i /\ B_i) in +let Adder(A,B,S,C,n) := /\i=1..n (Sum(A,B,S,C,i) /\ Carry(A,B,C,i)) /\ ~C_1 in + +let Zero(A,n) := /\i=1..n ~A_i in +let One(A,n) := A_1 /\ /\i=1..n ~A_i+1 in +let Two(A,n) := ~A_1 /\ A_2 /\ /\i=1..n ~A_i+2 in +let Three(A,n) := A_1 /\ A_2 /\ /\i=1..n ~A_i+2 in +let Four(A,n) := ~A_1 /\ ~A_2 /\ A_3 /\ /\i=1..n ~A_i+3 in +let Five(A,n) := A_1 /\ ~A_2 /\ A_3 /\ /\i=1..n ~A_i+3 in + +let LastBitNull() := ~X_n+1 /\ ~Y_n+1 in + +LastBitNull() +/\ One(N1,n+1) /\ Five(N2,n+1) /\ Three(N3,n+1) /\ Four(N4,n+1) +/\ Adder(X,Y,XpY,T1,n+1) +/\ LowerOrEqual(T2,N1,XpY,n+1) +/\ LowerOrEqual(T3,XpY,N2,n+1) +/\ GreaterOrEqual(T4,X,N3,n+1) +/\ GreaterOrEqual(T5,Y,N4,n+1) +| n>=0 + +// vim:ft=regstab + + diff --git a/benchmarks/Regstab/propositional/ex1.stab b/benchmarks/Regstab/propositional/ex1.stab new file mode 100644 index 0000000..40f368a --- /dev/null +++ b/benchmarks/Regstab/propositional/ex1.stab @@ -0,0 +1,5 @@ +//expected: sat + +P_1 /\ P_2 + +// vim:ft=regstab diff --git a/benchmarks/Regstab/propositional/ex2.stab b/benchmarks/Regstab/propositional/ex2.stab new file mode 100644 index 0000000..c682d10 --- /dev/null +++ b/benchmarks/Regstab/propositional/ex2.stab @@ -0,0 +1,5 @@ +//expected: sat + +P_1 /\ (Q_1 \/ ~P_1) + +// vim:ft=regstab diff --git a/benchmarks/SPASS-FD/FD_addition.in b/benchmarks/SPASS-FD/FD_addition.in new file mode 100644 index 0000000..a725e12 --- /dev/null +++ b/benchmarks/SPASS-FD/FD_addition.in @@ -0,0 +1,65 @@ +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 40. +% +% % number of calls to fixpoint : 1 +% S_init : +% (3: [ +(v0,0) != v0 if n = v0 ]. +% ) +% S_loop : +% (9: [ +(v0,0) != v0 if n = s(v0) ]. +% ) +% The empty clauses : +% (8: [ n = 0 ]. +% 13: [ n = s(0) ]. +% ) max_rank 2 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=40. Generated=399. Kept=77. proofs=1. +% Usable=39. Sos=31. Demods=2. Limbo=0, Disabled=10. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=243. Back_subsumed=7. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=2 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=3071. Demod_rewrites=379. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=658. Nonunit_bsub_feature_tests=326. +% Megabytes=0.12. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== + + + +%Simple example from Spass-FD +set(prolog_style_variables). +assign(max_given, 2300). +%set(raw). +set(index_flat). +%set(print_gen). +set(superind). +set(cycle1). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). + +0 + Y = Y . + X+Y != Z | s(Z) = s(X) + Y . +N(X) | -(X + 0 = X). + + +end_of_list. \ No newline at end of file diff --git a/benchmarks/SPASS-FD/FD_even.in b/benchmarks/SPASS-FD/FD_even.in new file mode 100644 index 0000000..960e64a --- /dev/null +++ b/benchmarks/SPASS-FD/FD_even.in @@ -0,0 +1,30 @@ +%Simple example from Spass-FD +% Sat +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +N(X) | -even(X). +even(0). +N(s(0)). +even(X) -> even1(s(X)). +even(s(X)) <-> even1(X). + + +end_of_list. \ No newline at end of file diff --git a/benchmarks/SPASS-FD/FD_intOrder.in b/benchmarks/SPASS-FD/FD_intOrder.in new file mode 100644 index 0000000..4f63406 --- /dev/null +++ b/benchmarks/SPASS-FD/FD_intOrder.in @@ -0,0 +1,64 @@ +% ============================== PROOF ================================= +% +% % Proof 1 at 0.01 (+ 0.00) seconds. +% % Given clauses 16. +% +% % number of calls to fixpoint : 1 +% S_init : +% (5: [ -H(v0,v0) if n = v0 ]. +% ) +% S_loop : +% (12: [ -H(v0,v0) if n = s(v0) ]. +% ) +% The empty clauses : +% (11: [ n = 0 ]. +% 14: [ n = s(0) ]. +% ) max_rank 3 +% +% ============================== end of proof ========================== +% +% ============================== STATISTICS ============================ +% +% Given=16. Generated=23. Kept=20. proofs=1. +% Usable=16. Sos=4. Demods=0. Limbo=0, Disabled=5. Hints=0. +% Kept_by_rule=0, Deleted_by_rule=0. +% Forward_subsumed=3. Back_subsumed=0. +% Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. +% New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. +% Demod_attempts=0. Demod_rewrites=0. +% Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. +% Nonunit_fsub_feature_tests=17. Nonunit_bsub_feature_tests=12. +% Megabytes=0.05. +% User_CPU=0.01, System_CPU=0.00, Wall_clock=0. +% +% ============================== end of statistics ===================== +% +% ============================== end of search ========================= + + +%Simple example from Spass-FD +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +set(binary_resolution). +set(ordered_res). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). + +G(s(0), 0). +G(X,Y) -> G(s(X),s(Y)). +N(X) | -H(X,X). +H(X,Y) <-> G(s(X),Y). + +end_of_list. \ No newline at end of file diff --git a/benchmarks/SPASS-FD/even.in b/benchmarks/SPASS-FD/even.in new file mode 100644 index 0000000..4c9ebd2 --- /dev/null +++ b/benchmarks/SPASS-FD/even.in @@ -0,0 +1,21 @@ +% Unsat OK +%assign(max_seconds, 1). +%set(raw). +%clear(auto_inference). +set(prolog_style_variables). +set(print_gen). +set(binary_resolution). +%clear(ordered_res). +assign(max_given, 600). +assign(literal_selection, none). +clear(predicate_elim). + +formulas(sos). +N(X) | even(X). +even(0). +even(X) -> even1(s(X)). +even(s(X)) <-> even1(X). + + +end_of_list. + diff --git a/ladr/avltree.c b/ladr/avltree.c index 3714c17..255b733 100644 --- a/ladr/avltree.c +++ b/ladr/avltree.c @@ -342,8 +342,10 @@ a fatal error occurs. Avl_node avl_delete(Avl_node p, void *item, Ordertype (*compare) (void *, void *)) { - if (p == NULL) + if (p == NULL){ + p_clause(item); fatal_error("avl_delete, item not found"); + } else { Ordertype relation = (*compare)(item, p->item); diff --git a/ladr/clash.c b/ladr/clash.c index c9a08dd..e889ad4 100644 --- a/ladr/clash.c +++ b/ladr/clash.c @@ -259,7 +259,19 @@ Topform resolve(Clash first, Just_type rule) } r->justification = resolve_just(j, rule); upward_clause_links(r); - return r; + /********************************* Modif ******************/ + init_rank(r); + if (get_rank(nuc) != -1 && get_rank(r) > get_rank(nuc) +1 ) { + + //printf("new = %d", get_rank(r) ); + r->rank = -2; + //printf("nuc = %d", get_rank(nuc) ); + //printf("sat = %d", get_rank(sat) ); + + } + /*........................................*/ + + return r; } /* resolve */ /************* @@ -270,67 +282,67 @@ Topform resolve(Clash first, Just_type rule) static void clash_recurse(Clash first, - Clash p, - BOOL (*sat_test) (Literals), - Just_type rule, - void (*proc_proc) (Topform)) + Clash p, + BOOL (*sat_test) (Literals), + Just_type rule, + void (*proc_proc) (Topform)) { - if (p == NULL) { - /* All clashable literals have been mated, so construct the resolvent. */ - Topform resolvent = resolve(first, rule); - (*proc_proc)(resolvent); - } - else if (!p->clashable | p->clashed) - clash_recurse(first, p->next, sat_test, rule, proc_proc); - else { - Term fnd_atom; - fnd_atom = mindex_retrieve_first(p->nuc_lit->atom, p->mate_index, UNIFY, - p->nuc_subst, p->sat_subst, - FALSE, &(p->mate_pos)); - while (fnd_atom != NULL) { - Literals slit = atom_to_literal(fnd_atom); - if ((*sat_test)(slit)) { - p->clashed = TRUE; - p->flipped = FALSE; - p->sat_lit = slit; - clash_recurse(first, p->next, sat_test, rule, proc_proc); - p->clashed = FALSE; - } - fnd_atom = mindex_retrieve_next(p->mate_pos); - } - /* If the literal is an equality, try flipping it. */ - if (eq_term(p->nuc_lit->atom)) { - Term flip = top_flip(p->nuc_lit->atom); - fnd_atom = mindex_retrieve_first(flip, p->mate_index, UNIFY, - p->nuc_subst, p->sat_subst, - FALSE, &(p->mate_pos)); - while (fnd_atom != NULL) { - Literals slit = atom_to_literal(fnd_atom); - if ((*sat_test)(slit)) { - p->clashed = TRUE; - p->flipped = TRUE; - p->sat_lit = slit; - clash_recurse(first, p->next, sat_test, rule, proc_proc); - p->clashed = FALSE; + if (p == NULL) { + /* All clashable literals have been mated, so construct the resolvent. */ + Topform resolvent = resolve(first, rule); + (*proc_proc)(resolvent); + } + else if (!p->clashable | p->clashed) + clash_recurse(first, p->next, sat_test, rule, proc_proc); + else { + Term fnd_atom; + fnd_atom = mindex_retrieve_first(p->nuc_lit->atom, p->mate_index, UNIFY, + p->nuc_subst, p->sat_subst, + FALSE, &(p->mate_pos)); + while (fnd_atom != NULL) { + Literals slit = atom_to_literal(fnd_atom); + if ((*sat_test)(slit)) { + p->clashed = TRUE; + p->flipped = FALSE; + p->sat_lit = slit; + clash_recurse(first, p->next, sat_test, rule, proc_proc); + p->clashed = FALSE; + } + fnd_atom = mindex_retrieve_next(p->mate_pos); + } + /* If the literal is an equality, try flipping it. */ + if (eq_term(p->nuc_lit->atom)) { + Term flip = top_flip(p->nuc_lit->atom); + fnd_atom = mindex_retrieve_first(flip, p->mate_index, UNIFY, + p->nuc_subst, p->sat_subst, + FALSE, &(p->mate_pos)); + while (fnd_atom != NULL) { + Literals slit = atom_to_literal(fnd_atom); + if ((*sat_test)(slit)) { + p->clashed = TRUE; + p->flipped = TRUE; + p->sat_lit = slit; + clash_recurse(first, p->next, sat_test, rule, proc_proc); + p->clashed = FALSE; + } + fnd_atom = mindex_retrieve_next(p->mate_pos); + } + zap_top_flip(flip); + } + /* Built-in resolution with x=x. */ + if (neg_eq(p->nuc_lit)) { + Term alpha = ARG(p->nuc_lit->atom,0); + Term beta = ARG(p->nuc_lit->atom,1); + Trail tr = NULL; + if (unify(alpha, p->nuc_subst, beta, p->nuc_subst, &tr)) { + p->clashed = TRUE; + p->sat_lit = NULL; + clash_recurse(first, p->next, sat_test, rule, proc_proc); + p->clashed = FALSE; + undo_subst(tr); + } + } } - fnd_atom = mindex_retrieve_next(p->mate_pos); - } - zap_top_flip(flip); - } - /* Built-in resolution with x=x. */ - if (neg_eq(p->nuc_lit)) { - Term alpha = ARG(p->nuc_lit->atom,0); - Term beta = ARG(p->nuc_lit->atom,1); - Trail tr = NULL; - if (unify(alpha, p->nuc_subst, beta, p->nuc_subst, &tr)) { - p->clashed = TRUE; - p->sat_lit = NULL; - clash_recurse(first, p->next, sat_test, rule, proc_proc); - p->clashed = FALSE; - undo_subst(tr); - } - } - } } /* clash_recurse */ /************* diff --git a/ladr/clauses.c b/ladr/clauses.c index 457b8d7..9aa82d8 100644 --- a/ladr/clauses.c +++ b/ladr/clauses.c @@ -326,3 +326,8 @@ BOOL equality_in_clauses(Plist clauses) } } /* equality_in_clauses */ +/*PUBLIC*/ +/*Responds True if clause is an (alpha-C)Clause*/ +BOOL is_alpha_clause(Topform clause){ + return ; +} \ No newline at end of file diff --git a/ladr/clauses.h b/ladr/clauses.h index e707f0c..9f3d450 100644 --- a/ladr/clauses.h +++ b/ladr/clauses.h @@ -56,5 +56,6 @@ int most_literals(Plist clauses); BOOL pos_equality_in_clauses(Plist clauses); BOOL equality_in_clauses(Plist clauses); +BOOL is_alpha_clause(Topform clause); #endif /* conditional compilation of whole file */ diff --git a/ladr/di_tree.c b/ladr/di_tree.c index e3ca2e0..2f83af4 100644 --- a/ladr/di_tree.c +++ b/ladr/di_tree.c @@ -342,11 +342,14 @@ BOOL subsume_di_literals(Literals clit, Context subst, Literals d, Trail *trp) static BOOL subsumes_di(Literals c, Literals d, Context subst) { - Trail tr = NULL; - BOOL subsumed = subsume_di_literals(c, subst, d, &tr); - if (subsumed) - undo_subst(tr); - return subsumed; + Trail tr = NULL; + BOOL subsumed = subsume_di_literals(c, subst, d, &tr); + if (subsumed) + undo_subst(tr); + if ((!param_free_lit(c) && !param_free_lit(d)) || (param_free_lit(c) && param_free_lit(d)) ) // Modif + return subsumed; + else + return FALSE; } /* subsumes_di */ /************* @@ -358,28 +361,39 @@ BOOL subsumes_di(Literals c, Literals d, Context subst) static Topform di_tree_forward(Ilist vec, Di_tree node, Literals dlits, Context subst) { - BUMP_SUB_CALLS; - if (vec == NULL) { - Plist p = node->u.data; - while (p) { - Topform c = p->v; - Nonunit_fsub_tests++; - if (subsumes_di(c->literals, dlits, subst)) - return p->v; - p = p->next; - } - return NULL; - } - else { - void *datum = NULL; - Di_tree kid = node->u.kids; - /* kids are in increasing order; look at those <= vec->i */ - while (!datum && kid && kid->label <= vec->i) { - datum = di_tree_forward(vec->next, kid, dlits, subst); - kid = kid->next; - } - return datum; - } + BUMP_SUB_CALLS; + if (vec == NULL) { + Plist p = node->u.data; + while (p) { + Topform c = p->v; + Nonunit_fsub_tests++; + if (subsumes_di(c->literals, dlits, subst)) + + return p->v; + + + p = p->next; + } + return NULL; + } + else { + void *datum = NULL; + Di_tree kid = node->u.kids; + /* kids are in increasing order; look at those <= vec->i */ + while (!datum && kid && kid->label <= vec->i) { + datum = di_tree_forward(vec->next, kid, dlits, subst); + kid = kid->next; + } + if ((!param_free(datum) && !param_free_lit(dlits)) || (param_free(datum) && param_free_lit(dlits)) ) { //Modif + //printf("W "); + //p_clause(datum); + return datum; + } + else { + return NULL; + } + + } } /* di_tree_forward */ /************* @@ -397,6 +411,8 @@ Topform forward_feature_subsume(Topform d, Di_tree root) Ilist f = features(d->literals); Context subst = get_context(); Topform c = di_tree_forward(f, root, d->literals, subst); + //printf("T "); + //p_clause(c); free_context(subst); zap_ilist(f); return c; @@ -410,29 +426,29 @@ Topform forward_feature_subsume(Topform d, Di_tree root) static void di_tree_back(Ilist vec, Di_tree node, Literals clits, Context subst, - Plist *subsumees) + Plist *subsumees) { - BUMP_SUB_CALLS; - if (vec == NULL) { - Plist p = node->u.data; - while (p) { - Topform d = p->v; - Nonunit_bsub_tests++; - if (clits != d->literals && subsumes_di(clits, d->literals, subst)) - *subsumees = plist_prepend(*subsumees, d); - p = p->next; - } - } - else { - Di_tree kid = node->u.kids; - /* kids are in increasing order; look at those >= vec->i */ - while (kid && kid->label < vec->i) - kid = kid->next; - while (kid) { - di_tree_back(vec->next, kid, clits, subst, subsumees); - kid = kid->next; - } - } + BUMP_SUB_CALLS; + if (vec == NULL) { + Plist p = node->u.data; + while (p) { + Topform d = p->v; + Nonunit_bsub_tests++; + if (clits != d->literals && subsumes_di(clits, d->literals, subst)) + *subsumees = plist_prepend(*subsumees, d); + p = p->next; + } + } + else { + Di_tree kid = node->u.kids; + /* kids are in increasing order; look at those >= vec->i */ + while (kid && kid->label < vec->i) + kid = kid->next; + while (kid) { + di_tree_back(vec->next, kid, clits, subst, subsumees); + kid = kid->next; + } + } } /* di_tree_back */ /************* diff --git a/ladr/glist.c b/ladr/glist.c index 833af11..1456d73 100644 --- a/ladr/glist.c +++ b/ladr/glist.c @@ -17,7 +17,7 @@ */ #include "glist.h" - +#include "topform.c" /* * memory management */ @@ -543,16 +543,22 @@ Remove the first occurrence of a pointer from a Plist. /* PUBLIC */ Plist plist_remove(Plist p, void *v) { - if (p == NULL) - fatal_error("plist_remove: pointer not found"); + + if (p == NULL){ + + fatal_error("plist_remove: pointer not found"); + + } if (p->v == v) { + Plist x = p; p = p->next; free_plist(x); return p; } else { + p->next = plist_remove(p->next, v); return p; } @@ -2017,3 +2023,127 @@ int multiset_occurrences(I2list m, int i) return (a == NULL ? 0 : a->j); } /* multiset_occurrences */ +/********************************** MODIF .......*/ +BOOL isEmpty(Plist p){ + return (p == NULL); +} + +/* PUBLIC */ +void p_plist_param(Plist p) +{ + printf( "("); + for (; p != NULL; p = p->next) { + Topform t=(Topform)p->v; + p_clause_param(t); + } + printf(") "); + +} /* fprint_ilist */ + +/* DOCUMENTATION + The list of integers is printed to FILE *fp like this: (4 5 1 3), + without a newline. + */ + +/* PUBLIC */ +void p_plist(Plist p) +{ + printf( "("); + for (; p != NULL; p = p->next) { + Topform t=(Topform)p->v; + p_clause(t); + } + printf(") "); + +} /* fprint_ilist */ + +/*.........................*/ +Plist plist_remove_clause(Plist p, void *v) +{ + // + if (p == NULL){ + return NULL; + //fatal_error("plist_remove_clause: remove from empty plist"); + + } + Topform v1 =p->v; + Topform v2 = (Topform)v; + if (clause_ident_order(v1, v2)) { + + Plist x = p; + p = p->next; + free_plist(x); + return p; + } + else { + + p->next = plist_remove_clause(p->next, v); + return p; + } +} +/********************/ +Plist plist_remove_plist(Plist lst, Plist q){ + if (lst == NULL) { + fatal_error("plist_remove_plist: remove from empty plist"); + } + Plist p,res; + res=lst; + if(q == NULL) + return lst; + for (p = q; p; p = p->next){ + res = plist_remove_clause(res, p->v); + + } + return res; +} +/* PUBLIC */ +/*return True if a Plist lst contains a topform u*/ +BOOL plist_member_clause(Plist lst, void *u) +{ + if (lst == NULL) + return FALSE; + else{ + Topform v1 =lst->v; + Topform v2 = (Topform)u; + /*if(get_rank(v1) == 1){ + printf("Begin"); + p_clause(v2); + p_clause(v1); + }*/ + if (clause_ident_order(v1, v2)){ + //printf(" egal "); + + return TRUE; + } + else{ + //printf(" pasegal "); + + return plist_member_clause(lst->next, v2); + } + } +} /* plist_member_clause */ +/* PUBLIC */ +/*return True if a Plist lst contains a Plist small*/ +BOOL plist_member_plist(Plist big, Plist small) +{ + if (big == NULL) + return FALSE; + else{ + if(small == NULL){ + return TRUE; + } + else{ + + if (!plist_member_clause(big, small->v)){ + //printf(" egal "); + return FALSE; + } + else{ + //p_clause(small->v); + //printf(" pasegal "); + + return plist_member_plist(big, small->next); + } + } + } +}/* plist_member_plist */ \ No newline at end of file diff --git a/ladr/glist.h b/ladr/glist.h index f0c0430..0e82731 100644 --- a/ladr/glist.h +++ b/ladr/glist.h @@ -21,6 +21,7 @@ #include "order.h" #include "string.h" +//#include "topform.h" /* INTRODUCTION This package handles @@ -234,5 +235,15 @@ I2list multiset_union(I2list a, I2list b); Ilist multiset_to_set(I2list m); int multiset_occurrences(I2list m, int i); +/**********************MODIF*/ +BOOL isEmpty(Plist p); + +void p_plist_param(Plist p); + +void p_plist(Plist p); +Plist plist_remove_clause(Plist p, void *v); +Plist plist_remove_plist(Plist lst, Plist q); +BOOL plist_member_clause(Plist lst, void *v); +BOOL plist_member_plist(Plist big, Plist small); #endif /* conditional compilation of whole file */ diff --git a/ladr/hash.h b/ladr/hash.h index 43f5719..98cb0a6 100644 --- a/ladr/hash.h +++ b/ladr/hash.h @@ -51,4 +51,6 @@ void hash_destroy(Hashtab h); void hash_info(Hashtab h); + + #endif /* conditional compilation of whole file */ diff --git a/ladr/just.c b/ladr/just.c index bd5c2ed..8b54c0f 100644 --- a/ladr/just.c +++ b/ladr/just.c @@ -1646,6 +1646,147 @@ Plist get_clause_ancestors(Topform c) return ancestors; } /* get_clause_ancestors */ +/****************************** MODIF*****************************/ +/* PUBLIC */ + + /* ...................................... + + //* iflat + ......................................*/ + +/* iflat return true if c is index_flat, false otherwise. + since we have the rank I of c, we just have to check whether the parameter depth is equal to I + */ + +BOOL iflat(int I, Topform c){ + Literals lit; + Term t; + if (false_clause(c->literals)) { + return FALSE; + } + else{ + for(lit = c->literals; lit != NULL; lit = lit->next){ + + t = lit->atom; + if (param_term(t)){ + return ((term_depth(t)-1)==I); + + } + + } + + p_clause (c); + fatal_error(" just.c: iflat : problem free param clause"); + } +} +/************** iflat ************************/ +static +Plist get_clanc_rank(int id, Plist anc, int rank) +{ + Topform c = find_clause_by_id(id); + //printf("ANC =");p_plist(anc); + if (c == NULL) { + printf("get_clanc_rank, clause with id=%d not found.\n", id); + fatal_error("get_clanc_rank, clause not found."); + } + + if (!plist_member_clause(anc, c)) { + Ilist parents, p; + if(get_rank(c) == rank){ + anc = insert_clause_into_plist(anc, c, TRUE); + } + parents = get_parents(c->justification, TRUE); + + for (p = parents; p; p = p->next) { + + Topform cl = find_clause_by_id(p->i); + if(get_rank(cl) >= rank ){ + anc = get_clanc_rank(p->i, anc, rank); + + } + } + zap_ilist(parents); + + } + //printf("NN =");p_plist(anc); + return anc; +} /* get_clanc_rank */ + +/*.........................*/ +Plist get_clause_ancestors_ofrank(Topform c, int rank) +{ + Plist ancestors = get_plist(); + ancestors = get_clanc_rank(c->id, NULL, rank); + //printf("anc ");p_plist(ancestors); + ancestors = plist_remove_clause(ancestors, c); + + return ancestors; +} /* get_clause_ancestors */ + +Plist get_clause_ancestors_ofrank2(Topform c, int rank, BOOL index_flat) +{ + Plist q; + Plist ancestors =NULL; + Plist clause_ancestors = get_clause_ancestors(c); + //printf("ss0");p_plist(clause_ancestors);printf("ss1"); + for (q = clause_ancestors; q; q = q->next) { + Topform d=(Topform)q->v; + //p_clause(d);printf("tt rank = %d I = %d ", get_rank(d), I ); + if (get_rank(d)==rank) { + if (index_flat) { + if (iflat(rank,d)) { + ancestors = insert_clause_into_plist(ancestors, d, TRUE); + } + } + else { + ancestors = insert_clause_into_plist(ancestors, d, TRUE); + } + //printf("B"); + } + } + + return ancestors; +} /* get_clause_ancestors_ofrank2 */ + + +Plist get_ancestors_of_rank2(int I, Plist EmptyCl, BOOL index_flat){ + Plist p, ancestors,q; + ancestors=NULL; + + Topform c,d; + + for (p = EmptyCl; p; p = p->next) { + c = (Topform)p->v; + //ancestors = get_clanc_(c->id, ancestors, I); + Plist clause_ancestors = get_clause_ancestors(c); + //printf("ss0");p_plist(clause_ancestors);printf("ss1"); + for (q = clause_ancestors; q; q = q->next) { + d=(Topform)q->v; + //p_clause(d);printf("tt rank = %d I = %d ", get_rank(d), I ); + if (get_rank(d)==I) { + if (!plist_member_clause(ancestors, d) && !pureparam_cst_topform(d)){ // && !clause_ident_order(c, d)) { + if (index_flat) { + if (iflat(I,d)) { + ancestors = insert_clause_into_plist(ancestors, d, TRUE); + } + } + else { + ancestors = insert_clause_into_plist(ancestors, d, TRUE); + } + + + } + //printf("B"); + } + } + + } + + //printf("t0");p_plist(ancestors);printf("t1"); + return ancestors; +} + +/**********************************************************/ /************* * * proof_length() diff --git a/ladr/just.h b/ladr/just.h index 53e05a5..a6c1a9c 100644 --- a/ladr/just.h +++ b/ladr/just.h @@ -231,4 +231,10 @@ BOOL has_copy_flip_just(Topform c); void sb_tagged_write_just(String_buf sb, Just just, I3list map); +/**********************************************MODIF***********/ +BOOL iflat(int I, Topform c); +Plist get_clause_ancestors_ofrank(Topform c, int rank); +Plist get_ancestor_of_rank(int I, Plist EmptyCl); +Plist get_ancestors_of_rank2(int I, Plist EmptyCl,BOOL index_flat); +Plist get_clause_ancestors_ofrank2(Topform c, int rank, BOOL index_flat); #endif /* conditional compilation of whole file */ diff --git a/ladr/ladr-1.moved-aside/loop.h b/ladr/ladr-1.moved-aside/loop.h new file mode 100644 index 0000000..f2f0e77 --- /dev/null +++ b/ladr/ladr-1.moved-aside/loop.h @@ -0,0 +1,10 @@ +/* + * loop.h + * + * + * Created by Abdelkader kersani on 22/05/12. + * Copyright 2012 LIG-CNRS. All rights reserved. + * + */ + +BOOL Fixed_Point(int i, int j, Ilist Si, Ilist Sij); \ No newline at end of file diff --git a/ladr/ladr.h b/ladr/ladr.h index 0577edd..a23e442 100644 --- a/ladr/ladr.h +++ b/ladr/ladr.h @@ -31,3 +31,4 @@ #include "definitions.h" #include "dollar.h" #include "top_input.h" +//#include "loop.h" \ No newline at end of file diff --git a/ladr/lindex.c b/ladr/lindex.c index 904921c..dec3ba4 100644 --- a/ladr/lindex.c +++ b/ladr/lindex.c @@ -154,7 +154,8 @@ void lindex_destroy(Lindex ldx) } /* lindex_destroy */ /************* - * + *assign(literal_selection, none). + * lindex_update() * *************/ @@ -166,13 +167,17 @@ This routine indexes (or unindexes) all literals of a clause. /* PUBLIC */ void lindex_update(Lindex ldx, Topform c, Indexop op) { - Literals lit; - for (lit = c->literals; lit != NULL; lit = lit->next) { - if (lit->sign) - mindex_update(ldx->pos, lit->atom, op); - else - mindex_update(ldx->neg, lit->atom, op); - } + Literals lit; + for (lit = c->literals; lit != NULL; lit = lit->next) { + if (!param_term(lit->atom)) { + + + if (lit->sign) + mindex_update(ldx->pos, lit->atom, op); + else + mindex_update(ldx->neg, lit->atom, op); + } + } } /* lindex_update */ /************* diff --git a/ladr/literals.c b/ladr/literals.c index f0e255f..f0889ba 100644 --- a/ladr/literals.c +++ b/ladr/literals.c @@ -782,6 +782,8 @@ BOOL true_clause(Literals lits) return true_clause(lits->next); } /* true_clause */ + + /************* * * complementary_scan() @@ -926,14 +928,21 @@ Identical clauses, including order of literals and variable numbering. /* PUBLIC */ BOOL clause_ident(Literals lits1, Literals lits2) { + if (lits1 == NULL) return lits2 == NULL; else if (lits2 == NULL) return FALSE; - else if (lits1->sign != lits2->sign) + else if (lits1->sign != lits2->sign){ + //printf("s0 %d ", lits1->sign ); + // printf("s1 %d ", lits2->sign ); + return FALSE; - else if (!term_ident(lits1->atom, lits2->atom)) + }else if (!term_ident(lits1->atom, lits2->atom)){ + return FALSE; + + } else return clause_ident(lits1->next, lits2->next); } /* clause_ident */ @@ -1182,3 +1191,211 @@ Ilist pos_predicates(Ilist p, Literals lits) return p; } /* pos_predicates */ +/********************************MODIF************************************/ +/************* + * + * false_clause() + * + *************/ +/* + Does the clause contain a literal $T? + (This does not check for complementary literals, -$F, or x=x.) + */ + +/* PUBLIC */ +BOOL false_clause(Literals lits) +{ + if (lits == NULL){ + + return TRUE; + } + else if (lits->sign && false_term(lits->atom)){ + return TRUE; + } + else { + + return FALSE; + } + + + +} /* false_clause */ + +/* + return the parameter literal + */ + +Literals param_of_topform(Literals lits){ + Literals l, param; + for (l = lits; l; l = l->next) { + if (param_term(l->atom)) { + param=copy_literal(l); + param->next = NULL; + return param; + } + } + + +} + +/************* + * + * remove_param_literals() + * + *************/ + +/* DOCUMENTATION + */ + +/* PUBLIC */ +Literals remove_param_literals(Literals l) +{ + if (l == NULL) + return NULL; + else { + l->next = remove_param_literals(l->next); + if (!param_term(l->atom)) + return l; + else { + Literals m = l->next; + free_literals(l); + return m; + } + } +} /* remove_param_literals */ + +/************* + * + * count_literal() + * + *************/ + +/* DOCUMENTATION + Return the number of literal of a clause, counting from 1. + */ + +/* PUBLIC */ +int count_literal(Literals lits) +{ + if (lits == NULL) + return 0; + else return 1 + count_literal(lits->next); +} /* count_literal */ + +BOOL include(Literals lits, Literals lit){ + //printf("k1 "); p_term(lits->atom); p_term(lit->atom) ; printf(" k2\n"); + if (lits == NULL) { + return FALSE; + }else { + if (term_ident(lits->atom, lit->atom) && (lits->sign == lit->sign)) { + //printf("A"); + return TRUE; + }else { + //printf("B"); + return include(lits->next, lit); + } + + } + +} + +BOOL literals_ident(Literals lits1, Literals lits2) +{//lits1->next->sign= TRUE; + if (lits2 == NULL) { + return TRUE; + } + else{ + if (!include(lits1, ith_literal(lits2,1))){ + + //printf("clause ident %d ", clause_ident(lits1->next, ith_literal(lits2,1))); + //printf("kk "); p_term(lits1->next->atom); p_term(ith_literal(lits2,1)->atom) ; printf(" kk\n"); + //printf("now %d ", include(lits1, ith_literal(lits2,1))); + return FALSE; + } + else return literals_ident(lits1, lits2->next); + } + +} + +BOOL loop_literals(Literals lits){ + if (count_literal(lits) >1) { + return FALSE; + }else { + if (!param_term(lits->atom)) + return FALSE; + else { + return variable_term(lits->atom); + } + + } + +} + +/*int depth_param(Literals l){ + return term_depth(l->atom); +} +int max_depth(Literals l){ + Literals temp; + return max_depth(l->Literals +}*/ + +/************************** *************/ +/* Retourne vrai si la clause n'a pas de parametre \alpha */ +BOOL param_free_lit(Literals l){ + Term t; + Literals lit; + if (l==NULL) { + return TRUE; + } + + for (lit = l; lit != NULL; lit = lit->next){ + t = lit->atom; + if (param_term(t)) { + return FALSE; + } + } + return TRUE; +} + +/*********************/ +int compute_rank_lit(Literals l){ + int depth_param =0; + int max_depth = 0; + BOOL N=FALSE; + //printf("couoooooooooooooooooo"); + + if (param_free_lit(l)) { + + return -1; + } + else{ + Literals lit; + Term t; + //printf("couoooooooooooooooooo"); + for(lit = l; lit != NULL; lit = lit->next){ + + t = lit->atom; + if (param_term(t)){ + depth_param = term_depth(t); + + } + else{ + if (succ_occurs_in(t)){// if "s" occurs once + + max_depth = 1; + } + } + + } + + + + //printf(" max_depth = %d ", max_depth); + //p_clause(p); + //printf("depth_param = %d ", depth_param); + return depth_param - max_depth ; + } +} +/************************/ + +//******************************* diff --git a/ladr/literals.h b/ladr/literals.h index 9b27d5d..ac2911f 100644 --- a/ladr/literals.h +++ b/ladr/literals.h @@ -147,4 +147,24 @@ Term term_at_position(Literals lits, Ilist pos); Ilist pos_predicates(Ilist p, Literals lits); +/****************************MODIF*************/ +BOOL false_clause(Literals lits); + +Literals param_of_topform(Literals lits); + +Literals remove_param_literals(Literals l); + +int count_literal(Literals lits); + +BOOL include(Literals lits, Literals lit); + +BOOL literals_ident(Literals lits1, Literals lits2); + +BOOL loop_literals(Literals lits); + +BOOL param_free_lit(Literals l); + +int compute_rank_lit(Literals l); + + #endif /* conditional compilation of whole file */ diff --git a/ladr/maximal.c b/ladr/maximal.c index 1f00d87..6577283 100644 --- a/ladr/maximal.c +++ b/ladr/maximal.c @@ -52,19 +52,33 @@ void init_maximal(void) static BOOL greater_literals(Literals l1, Literals l2) { - Term a1 = l1->atom; - Term a2 = l2->atom; - Ordertype p = sym_precedence(SYMNUM(a1), SYMNUM(a2)); - if (p == GREATER_THAN) - return TRUE; - else if (p == LESS_THAN) - return FALSE; - else if (SYMNUM(a1) != SYMNUM(a2)) - return FALSE; - else if (is_eq_symbol(SYMNUM(a1))) - return greater_multiset_current_ordering(a1, a2); - else - return term_greater(a1, a2, FALSE); /* LPO, RPO, KBO */ + Term a1 = l1->atom; + Term a2 = l2->atom; + // ************* Modif **************** + if(succ_occurs_in(a1) && !succ_occurs_in(a2)){ + //printf("t1 "); p_term(a1);printf("t1 "); + //printf("t2 "); p_term(a2); printf("t2 "); + return TRUE; + } + else if(!succ_occurs_in(a1) && succ_occurs_in(a2)){ + //printf("k1 "); p_term(a1);printf("k1 "); + //printf("k2 "); p_term(a2); printf("k2 "); + + return FALSE; + } + else{ + Ordertype p = sym_precedence(SYMNUM(a1), SYMNUM(a2)); + if (p == GREATER_THAN) + return TRUE; + else if (p == LESS_THAN) + return FALSE; + else if (SYMNUM(a1) != SYMNUM(a2)) + return FALSE; + else if (is_eq_symbol(SYMNUM(a1))) + return greater_multiset_current_ordering(a1, a2); + else + return term_greater(a1, a2, FALSE); /* LPO, RPO, KBO */ + } } /* greater_literals */ /************* @@ -82,16 +96,29 @@ This version does not use a flag. /* PUBLIC */ BOOL max_lit_test(Literals lits, Literals lit) { - /* If there is a greater literal of ANY sign, return FALSE. */ - Literals l2 = lits; - BOOL maximal = TRUE; - while (l2 && maximal) { - if (lit != l2 && greater_literals(l2, lit)) - maximal = FALSE; - else - l2 = l2->next; - } - return maximal; + BOOL maximal = TRUE; + //Modif + if (param_term(lit->atom)) { + return FALSE; + } + else{ + /* If there is a greater literal of ANY sign, return FALSE. */ + Literals l2 = lits; + + while (l2 && maximal) { + //printf("l2 = "); p_term (l2->atom); + //printf("lit = "); p_term (l2->atom); + //printf("param_term = %d ",param_term(l2->atom)); + //printf("greater (l2,lit) = %d ", greater_literals(l2, lit)); + //printf("(lit!=l2) = %d ",lit != l2); + if (lit != l2 && !param_term(l2->atom) && greater_literals(l2, lit)) //Modif + maximal = FALSE; + else + l2 = l2->next; + } + } + //printf(" l ");p_term(lit->atom);printf("max = %d", maximal);printf(" l \n"); + return maximal; } /* max_lit_test */ /************* @@ -109,16 +136,22 @@ This version does not use a flag. /* PUBLIC */ BOOL max_signed_lit_test(Literals lits, Literals lit) { - /* If there is a greater literal of the same sign, return FALSE. */ - Literals l2 = lits; - BOOL maximal = TRUE; - while (l2 && maximal) { - if (lit != l2 && lit->sign == l2->sign && greater_literals(l2, lit)) - maximal = FALSE; - else - l2 = l2->next; - } - return maximal; + BOOL maximal = TRUE; + //Modif + if (param_term(lit->atom)) { + return FALSE; + } + else{ + /* If there is a greater literal of the same sign, return FALSE. */ + Literals l2 = lits; + while (l2 && maximal) { + if (lit != l2 && lit->sign == l2->sign && !param_term(l2->atom) && greater_literals(l2, lit)) + maximal = FALSE; + else + l2 = l2->next; + } + } + return maximal; } /* max_signed_lit_test */ /************* @@ -141,10 +174,14 @@ void mark_maximal_literals(Literals lits) /* Note: we mark the atom, not the literal. */ for (lit = lits; lit; lit = lit->next) { - if (max_lit_test(lits, lit)) + if (max_lit_test(lits, lit)){ + //printf("max lit = "); p_term(lit->atom); term_flag_set(lit->atom, Maximal_flag); - if (max_signed_lit_test(lits, lit)) - term_flag_set(lit->atom, Maximal_signed_flag); + } + //if (max_signed_lit_test(lits, lit)){ + // printf("lit signed = "); p_term(lit->atom); + // term_flag_set(lit->atom, Maximal_signed_flag); + //} } } /* mark_maximal_literals */ @@ -163,10 +200,16 @@ or FULL_CHECK (do the full comparicon). /* PUBLIC */ BOOL maximal_literal(Literals lits, Literals lit, int check) { - if (check == FLAG_CHECK) + + + if (check == FLAG_CHECK){ + //printf(" max lit flag "); p_term(lit->atom); return term_flag(lit->atom, Maximal_flag); - else + } + else{ + //printf(" max lit "); p_term(lit->atom); return max_lit_test(lits, lit); + } } /* maximal_literal */ /************* diff --git a/ladr/mindex.c b/ladr/mindex.c index 47e9835..008eb21 100644 --- a/ladr/mindex.c +++ b/ladr/mindex.c @@ -468,12 +468,12 @@ Term mindex_retrieve_first(Term t, Mindex mdx, Querytype qtype, Mindex_pos *ppos) { Mindex_pos pos; - if ((mdx->index_type == DISCRIM_WILD || mdx->index_type == DISCRIM_BIND) && qtype != GENERALIZATION) return NULL; else { + pos = get_mindex_pos(); pos->index = mdx; pos->query_type = qtype; @@ -485,7 +485,6 @@ Term mindex_retrieve_first(Term t, Mindex mdx, Querytype qtype, pos->btu_position = NULL; pos->btm_position = NULL; pos->partial_match = partial_match; - if (mdx->index_type == FPA) pos->fpa_position = NULL; else if (mdx->index_type == DISCRIM_WILD) @@ -494,7 +493,6 @@ Term mindex_retrieve_first(Term t, Mindex mdx, Querytype qtype, pos->discrim_position = NULL; else if (mdx->index_type == LINEAR) pos->linear_position = mdx->linear_first; - *ppos = pos; return mindex_retrieve_next(pos); } diff --git a/ladr/paramod.c b/ladr/paramod.c index 9a18a7e..3812ca6 100644 --- a/ladr/paramod.c +++ b/ladr/paramod.c @@ -244,37 +244,37 @@ BOOL from_parent_test(Literals from_lit, int check) static BOOL into_parent_test(Literals into_lit, int check) { - Topform into_parent = into_lit->atom->container; - if (into_lit->sign) { - /* into positive literal */ - if (Positive_inference) - return - positive_clause(into_parent->literals) && - (!Ordered_inference || - maximal_literal(into_parent->literals, into_lit, check)); - else - return - !exists_selected_literal(into_parent->literals) && - (!Ordered_inference || - maximal_literal(into_parent->literals, into_lit, check)); - } - else { - /* into negative literal */ - if (Positive_inference) { - if (exists_selected_literal(into_parent->literals)) - return selected_literal(into_lit); - else - return (!Ordered_inference || - maximal_signed_literal(into_parent->literals,into_lit,check)); - } - else { - if (exists_selected_literal(into_parent->literals)) - return selected_literal(into_lit); - else - return (!Ordered_inference || - maximal_literal(into_parent->literals, into_lit, check)); - } - } + Topform into_parent = into_lit->atom->container; + if (into_lit->sign) { + /* into positive literal */ + if (Positive_inference) + return + positive_clause(into_parent->literals) && + (!Ordered_inference || + maximal_literal(into_parent->literals, into_lit, check)); + else + return + !exists_selected_literal(into_parent->literals) && + (!Ordered_inference || + maximal_literal(into_parent->literals, into_lit, check)); + } + else { + /* into negative literal */ + if (Positive_inference) { + if (exists_selected_literal(into_parent->literals)) + return selected_literal(into_lit); + else + return (!Ordered_inference || + maximal_signed_literal(into_parent->literals,into_lit,check)); + } + else { + if (exists_selected_literal(into_parent->literals)) + return selected_literal(into_lit); + else + return (!Ordered_inference || + maximal_literal(into_parent->literals, into_lit, check)); + } + } } /* into_parent_test */ /************* @@ -373,6 +373,19 @@ void para_into(Literals from_lit, int from_side, Context cf, Ilist from_pos, copy_ilist(from_pos), into_clause, copy_ilist(into_pos)); + /**************************************Modif**********************/ + // Initialize the rank + init_rank(p); + // if the m.g.u is at least of the form s(s(x)) the clause won't be kept + //if (get_rank(into_clause) != -1 && (get_rank(p) > get_rank(into_clause) +1 || get_rank(p) > compute_rank_lit(from_lit) +1 )){ + if ((get_rank(into_clause) != -1 && get_rank(p) > get_rank(into_clause) +1 ) || (get_rank(p) < get_rank(into_clause)) ){ + p->rank =-2; + } + // if it's not an (alpha-C)-clause, p will be deleted in cl_process + if (!alpha_C_clause(p)) { + p->rank=-3; + } + /************************************************************/ (*proc_proc)(p); } undo_subst(tr); @@ -440,27 +453,27 @@ For nonoriented equality atoms, we go from and into both sides. /* PUBLIC */ void para_from_into(Topform from, Context cf, - Topform into, Context ci, - BOOL check_top, - void (*proc_proc) (Topform)) + Topform into, Context ci, + BOOL check_top, + void (*proc_proc) (Topform)) { - if (exists_selected_literal(from->literals)) - return; /* cannot para from clause with selected literals */ - else { - Literals from_lit; - for (from_lit = from->literals; from_lit; from_lit = from_lit->next) { - if (from_parent_test(from_lit, FLAG_CHECK)) { - Literals into_lit; - for (into_lit = into->literals; into_lit; into_lit = into_lit->next) { - if (into_parent_test(into_lit, FLAG_CHECK)) { - para_into_lit(from_lit,0,cf,into_lit,ci,check_top,proc_proc); /* from L */ - if (para_from_right(from_lit->atom)) - para_into_lit(from_lit,1,cf,into_lit,ci,check_top,proc_proc); /* from R */ - } + if (exists_selected_literal(from->literals)) + return; /* cannot para from clause with selected literals */ + else { + Literals from_lit; + for (from_lit = from->literals; from_lit; from_lit = from_lit->next) { + if (from_parent_test(from_lit, FLAG_CHECK)) { + Literals into_lit; + for (into_lit = into->literals; into_lit; into_lit = into_lit->next) { + if (into_parent_test(into_lit, FLAG_CHECK)) { + para_into_lit(from_lit,0,cf,into_lit,ci,check_top,proc_proc); /* from L */ + if (para_from_right(from_lit->atom)) + para_into_lit(from_lit,1,cf,into_lit,ci,check_top,proc_proc); /* from R */ + } + } + } + } } - } - } - } } /* para_from_into */ /************* diff --git a/ladr/parse.c b/ladr/parse.c index 548047d..10bad24 100644 --- a/ladr/parse.c +++ b/ladr/parse.c @@ -1316,7 +1316,7 @@ Term sread_term(String_buf sb, FILE *fout) fprint_parse_error(fout, tp.error_message, sb, tp.start_error, tp.end_error); free_token_list(tp.tok); - fatal_error("sread_term error"); + fatal_error("sread_term error0"); } else if (tp.tok != NULL) { fprint_parse_error(fout, diff --git a/ladr/res.out b/ladr/res.out new file mode 100644 index 0000000..e69de29 diff --git a/ladr/resolve.c b/ladr/resolve.c index 285545b..1c8edcf 100644 --- a/ladr/resolve.c +++ b/ladr/resolve.c @@ -127,58 +127,58 @@ static void hyper_sat_atom(BOOL flipped, Literals slit, Term atom, int pos_or_neg, Lindex idx, void (*proc_proc) (Topform)) { - BOOL positive = (pos_or_neg == POS_RES); - Context sat_subst = get_context(); - Context nuc_subst = get_context(); - Term fnd_atom; - Mindex_pos mate_pos; - fnd_atom = mindex_retrieve_first(atom, - positive ? idx->neg : idx->pos, - UNIFY, - sat_subst, nuc_subst, - FALSE, &mate_pos); - while (fnd_atom) { /* loop through found nuclei atoms */ - /* it must be in a nucleus because of the index used above */ - Topform nuc = fnd_atom->container; - Literals nuc_lit = atom_to_literal(fnd_atom); - Clash p = NULL; - Clash first = NULL; - Literals nlit; - for (nlit = nuc->literals; nlit; nlit = nlit->next) { - p = append_clash(p); - if (first == NULL) - first = p; - p->nuc_lit = nlit; - p->nuc_subst = nuc_subst; - if (nlit == nuc_lit) { - p->sat_lit = slit; - p->sat_subst = sat_subst; - p->clashable = TRUE; - p->clashed = TRUE; - p->flipped = flipped; - } - else { - if (!Production_mode) - p->clashable = positive ? !nlit->sign : nlit->sign; - else - p->clashable = (positive && - !nlit->sign && - !evaluable_predicate(SYMNUM(nlit->atom))); - if (p->clashable) { - p->mate_index = positive ? idx->pos : idx->neg; - p->sat_subst = get_context(); - } - } - } /* for each literal of nucleus */ - clash(first, - positive ? pos_hyper_sat_test : neg_hyper_sat_test, - HYPER_RES_JUST, - proc_proc); - zap_clash(first); - fnd_atom = mindex_retrieve_next(mate_pos); - } /* for each found nucleus atom */ - free_context(sat_subst); - free_context(nuc_subst); + BOOL positive = (pos_or_neg == POS_RES); + Context sat_subst = get_context(); + Context nuc_subst = get_context(); + Term fnd_atom; + Mindex_pos mate_pos; + fnd_atom = mindex_retrieve_first(atom, + positive ? idx->neg : idx->pos, + UNIFY, + sat_subst, nuc_subst, + FALSE, &mate_pos); + while (fnd_atom) { /* loop through found nuclei atoms */ + /* it must be in a nucleus because of the index used above */ + Topform nuc = fnd_atom->container; + Literals nuc_lit = atom_to_literal(fnd_atom); + Clash p = NULL; + Clash first = NULL; + Literals nlit; + for (nlit = nuc->literals; nlit; nlit = nlit->next) { + p = append_clash(p); + if (first == NULL) + first = p; + p->nuc_lit = nlit; + p->nuc_subst = nuc_subst; + if (nlit == nuc_lit) { + p->sat_lit = slit; + p->sat_subst = sat_subst; + p->clashable = TRUE; + p->clashed = TRUE; + p->flipped = flipped; + } + else { + if (!Production_mode) + p->clashable = positive ? !nlit->sign : nlit->sign; + else + p->clashable = (positive && + !nlit->sign && + !evaluable_predicate(SYMNUM(nlit->atom))); + if (p->clashable) { + p->mate_index = positive ? idx->pos : idx->neg; + p->sat_subst = get_context(); + } + } + } /* for each literal of nucleus */ + clash(first, + positive ? pos_hyper_sat_test : neg_hyper_sat_test, + HYPER_RES_JUST, + proc_proc); + zap_clash(first); + fnd_atom = mindex_retrieve_next(mate_pos); + } /* for each found nucleus atom */ + free_context(sat_subst); + free_context(nuc_subst); } /* hyper_sat_atom */ /************* @@ -191,17 +191,17 @@ static void hyper_satellite(Topform c, int pos_or_neg, Lindex idx, void (*proc_proc) (Topform)) { - Literals slit; - for (slit = c->literals; slit; slit = slit->next) { - if (!Ordered || maximal_literal(c->literals, slit, FLAG_CHECK)) { - hyper_sat_atom(FALSE, slit, slit->atom, pos_or_neg, idx, proc_proc); - if (pos_eq(slit)) { - Term flip = top_flip(slit->atom); - hyper_sat_atom(TRUE, slit, flip, pos_or_neg, idx, proc_proc); - zap_top_flip(flip); - } - } /* if sat is ok */ - } /* for each literal of satellite */ + Literals slit; + for (slit = c->literals; slit; slit = slit->next) { + if (!Ordered || maximal_literal(c->literals, slit, FLAG_CHECK)) { + hyper_sat_atom(FALSE, slit, slit->atom, pos_or_neg, idx, proc_proc); + if (pos_eq(slit)) { + Term flip = top_flip(slit->atom); + hyper_sat_atom(TRUE, slit, flip, pos_or_neg, idx, proc_proc); + zap_top_flip(flip); + } + } /* if sat is ok */ + } /* for each literal of satellite */ } /* hyper_satellite */ /************* @@ -212,36 +212,36 @@ void hyper_satellite(Topform c, int pos_or_neg, Lindex idx, static void hyper_nucleus(Topform c, int pos_or_neg, Lindex idx, - void (*proc_proc) (Topform)) + void (*proc_proc) (Topform)) { - BOOL positive = (pos_or_neg == POS_RES); - Clash p = NULL; - Clash first = NULL; - Literals lit; - Context nuc_subst = get_context(); - for (lit = c->literals; lit; lit = lit->next) { - p = append_clash(p); - if (first == NULL) - first = p; - if (!Production_mode) - p->clashable = positive ? !lit->sign : lit->sign; - else - p->clashable = (positive && - !lit->sign && - !evaluable_predicate(SYMNUM(lit->atom))); - p->nuc_lit = lit; - p->nuc_subst = nuc_subst; - if (p->clashable) { - p->mate_index = positive ? idx->pos : idx->neg; - p->sat_subst = get_context(); - } - } - clash(first, - positive ? pos_hyper_sat_test : neg_hyper_sat_test, - HYPER_RES_JUST, - proc_proc); - free_context(nuc_subst); - zap_clash(first); /* This also frees satellite contexts. */ + BOOL positive = (pos_or_neg == POS_RES); + Clash p = NULL; + Clash first = NULL; + Literals lit; + Context nuc_subst = get_context(); + for (lit = c->literals; lit; lit = lit->next) { + p = append_clash(p); + if (first == NULL) + first = p; + if (!Production_mode) + p->clashable = positive ? !lit->sign : lit->sign; + else + p->clashable = (positive && + !lit->sign && + !evaluable_predicate(SYMNUM(lit->atom))); + p->nuc_lit = lit; + p->nuc_subst = nuc_subst; + if (p->clashable) { + p->mate_index = positive ? idx->pos : idx->neg; + p->sat_subst = get_context(); + } + } + clash(first, + positive ? pos_hyper_sat_test : neg_hyper_sat_test, + HYPER_RES_JUST, + proc_proc); + free_context(nuc_subst); + zap_clash(first); /* This also frees satellite contexts. */ } /* hyper_nucleus */ /************* @@ -295,63 +295,63 @@ BOOL target_check(Literals lit, int target_constraint) static void ur_sat_atom(BOOL flipped, Topform c, int target_constraint, - Term sat_atom, Lindex idx, - void (*proc_proc) (Topform)) + Term sat_atom, Lindex idx, + void (*proc_proc) (Topform)) { - /* Assume C is a unit. */ - Context sat_subst = get_context(); - Context nuc_subst = get_context(); - Term fnd_atom; - Mindex_pos mate_pos; - Literals slit = c->literals; - - fnd_atom = mindex_retrieve_first(sat_atom, (slit->sign?idx->neg:idx->pos), - UNIFY, sat_subst, nuc_subst, - FALSE, &mate_pos); - while (fnd_atom) { - Topform nuc = fnd_atom->container; - int numlits = number_of_literals(nuc->literals); - if (numlits > 1 && numlits <= Ur_nucleus_limit && - (!Initial_nuclei || nuc->initial)) { - Literals fnd_lit = atom_to_literal(fnd_atom); - Literals target; - for (target=nuc->literals; target; target=target->next) { - if (target != fnd_lit && target_check(target, target_constraint)) { - - Clash p = NULL; - Clash first = NULL; - Literals nlit; - for (nlit = nuc->literals; nlit; nlit = nlit->next) { - p = append_clash(p); - if (first == NULL) - first = p; - p->nuc_lit = nlit; - p->nuc_subst = nuc_subst; - if (nlit == fnd_lit) { - p->sat_lit = slit; - p->sat_subst = sat_subst; - p->clashable = TRUE; - p->clashed = TRUE; - p->flipped = flipped; - } - else { - p->clashable = (nlit != target); - if (p->clashable) { - p->mate_index = (nlit->sign ? idx->neg : idx->pos); - p->sat_subst = get_context(); - } - } - } /* for each literal of nucleus */ - clash(first, unit_check, UR_RES_JUST, proc_proc); - zap_clash(first); - } - } /* for each target */ - } /* if we have a nuc */ - fnd_atom = mindex_retrieve_next(mate_pos); - } /* for each mate */ - free_context(sat_subst); - free_context(nuc_subst); + /* Assume C is a unit. */ + Context sat_subst = get_context(); + Context nuc_subst = get_context(); + Term fnd_atom; + Mindex_pos mate_pos; + Literals slit = c->literals; + + fnd_atom = mindex_retrieve_first(sat_atom, (slit->sign?idx->neg:idx->pos), + UNIFY, sat_subst, nuc_subst, + FALSE, &mate_pos); + while (fnd_atom) { + Topform nuc = fnd_atom->container; + int numlits = number_of_literals(nuc->literals); + if (numlits > 1 && numlits <= Ur_nucleus_limit && + (!Initial_nuclei || nuc->initial)) { + Literals fnd_lit = atom_to_literal(fnd_atom); + Literals target; + for (target=nuc->literals; target; target=target->next) { + if (target != fnd_lit && target_check(target, target_constraint)) { + + Clash p = NULL; + Clash first = NULL; + Literals nlit; + for (nlit = nuc->literals; nlit; nlit = nlit->next) { + p = append_clash(p); + if (first == NULL) + first = p; + p->nuc_lit = nlit; + p->nuc_subst = nuc_subst; + if (nlit == fnd_lit) { + p->sat_lit = slit; + p->sat_subst = sat_subst; + p->clashable = TRUE; + p->clashed = TRUE; + p->flipped = flipped; + } + else { + p->clashable = (nlit != target); + if (p->clashable) { + p->mate_index = (nlit->sign ? idx->neg : idx->pos); + p->sat_subst = get_context(); + } + } + } /* for each literal of nucleus */ + clash(first, unit_check, UR_RES_JUST, proc_proc); + zap_clash(first); + } + } /* for each target */ + } /* if we have a nuc */ + fnd_atom = mindex_retrieve_next(mate_pos); + } /* for each mate */ + free_context(sat_subst); + free_context(nuc_subst); } /* ur_sat_atom */ /************* @@ -383,37 +383,37 @@ void ur_satellite(Topform c, int target_constraint, Lindex idx, static void ur_nucleus(Topform c, int target_constraint, Lindex idx, - void (*proc_proc) (Topform)) + void (*proc_proc) (Topform)) { - if (number_of_literals(c->literals) > Ur_nucleus_limit || - (Initial_nuclei && !c->initial)) - return; - else { - Literals target; - for (target = c->literals; target; target = target->next) { - if (target_check(target, target_constraint)) { - Clash p = NULL; - Clash first = NULL; - Literals lit; - Context nuc_subst = get_context(); - for (lit = c->literals; lit; lit = lit->next) { - p = append_clash(p); - if (first == NULL) - first = p; - p->clashable = (lit != target); - p->nuc_lit = lit; - p->nuc_subst = nuc_subst; - if (p->clashable) { - p->mate_index = (lit->sign ? idx->neg : idx->pos); - p->sat_subst = get_context(); - } + if (number_of_literals(c->literals) > Ur_nucleus_limit || + (Initial_nuclei && !c->initial)) + return; + else { + Literals target; + for (target = c->literals; target; target = target->next) { + if (target_check(target, target_constraint)) { + Clash p = NULL; + Clash first = NULL; + Literals lit; + Context nuc_subst = get_context(); + for (lit = c->literals; lit; lit = lit->next) { + p = append_clash(p); + if (first == NULL) + first = p; + p->clashable = (lit != target); + p->nuc_lit = lit; + p->nuc_subst = nuc_subst; + if (p->clashable) { + p->mate_index = (lit->sign ? idx->neg : idx->pos); + p->sat_subst = get_context(); + } + } + clash(first, unit_check, UR_RES_JUST, proc_proc); + free_context(nuc_subst); + zap_clash(first); /* This also frees satellite contexts. */ + } + } } - clash(first, unit_check, UR_RES_JUST, proc_proc); - free_context(nuc_subst); - zap_clash(first); /* This also frees satellite contexts. */ - } - } - } } /* ur_nucleus */ /************* @@ -463,7 +463,8 @@ void xx_res(Literals lit, void (*proc_proc) (Topform)) undo_subst(tr); upward_clause_links(c); c->attributes = inheritable_att_instances(parent->attributes, subst); - + //Topform p1 = get_topform(); + //add_ancestors(parent); (*proc_proc)(c); } free_context(subst); @@ -514,6 +515,33 @@ void binary_resolvent(BOOL flipped, r->justification = resolve_just(j, BINARY_RES_JUST); upward_clause_links(r); +/********************** Modif *****************/ + // initialize the rank + // if the m.g.u is at least of the form s(s(x)) the clause won't be kept + init_rank(r); + if ((get_rank(nuc) != -1 && get_rank(r) > get_rank(nuc) +1) || (get_rank(sat) != -1 && get_rank(r) > get_rank(sat) +1)) { + + //printf("new = %d", get_rank(r) ); + r->rank = -2; + //printf("nuc = %d", get_rank(nuc) ); + //printf("sat = %d", get_rank(sat) ); + + } + if (get_rank(r) < get_rank(nuc) || get_rank(r) < get_rank(sat)) { + + //printf("new = %d", get_rank(r) ); + r->rank = -2; + //printf("nuc = %d", get_rank(nuc) ); + //printf("sat = %d", get_rank(sat) ); + + } + // if it's not an (alpha-C)-clause, r will be deleted in cl_process + if (!alpha_C_clause(r)) { + r->rank=-3; + } + //add_ancestors(nuc, sat, r); + +/******************************* End modif *************************************/ (*proc_proc)(r); } /* binary_resolvent */ @@ -527,40 +555,53 @@ void binary_resolvent(BOOL flipped, static BOOL binary_parent_test(Literals lit, int res_type, int check_type) -{ - Topform c = lit->atom->container; - - if (res_type == POS_RES) { /* positive resolution (one parent positive) */ - if (positive_clause(c->literals)) - return !Ordered || maximal_literal(c->literals, lit, check_type); - else if (lit->sign) - return FALSE; /* cannot resolve on pos literal in nonpos clause */ - else if (exists_selected_literal(c->literals)) - return selected_literal(lit); - else - return !Ordered || maximal_signed_literal(c->literals, lit, check_type); /* max neg */ - } - - else if (res_type == NEG_RES) { /* negative resolution (one parent neg) */ - if (negative_clause(c->literals)) - return !Ordered || maximal_literal(c->literals, lit, check_type); - else if (!lit->sign) - return FALSE; /* cannot resolve on neg literal in nonneg clause */ - else /* selection ignored for negative resolution */ - return !Ordered || maximal_signed_literal(c->literals, lit, check_type); /* max pos */ - } - - else { /* ANY_RES (not necessarily positive or negative resolution) */ - if (exists_selected_literal(c->literals)) { - if (lit->sign) - return FALSE; /* if any selected lits, cannot resolve on pos lit */ - else - return selected_literal(lit); - } - else - /* no selected literals in clause */ - return !Ordered || maximal_literal(c->literals, lit, check_type); - } +{ //Modif + /*if(param_term(lit->atom)){ //|| !succ_occurs_in(lit->atom)) + printf("not parent :"); + p_clause(lit->atom->container); + printf(" F"); + return FALSE; + } + else{*/ + Topform c = lit->atom->container; + //printf("c : ");p_clause(c); + if (res_type == POS_RES) { /* positive resolution (one parent positive) */ + if (positive_clause(c->literals)) + return !Ordered || maximal_literal(c->literals, lit, check_type); + else if (lit->sign) + return FALSE; /* cannot resolve on pos literal in nonpos clause */ + else if (exists_selected_literal(c->literals)) + return selected_literal(lit); + else + return !Ordered || maximal_signed_literal(c->literals, lit, check_type); /* max neg */ + } + + else if (res_type == NEG_RES) { /* negative resolution (one parent neg) */ + if (negative_clause(c->literals)) + return !Ordered || maximal_literal(c->literals, lit, check_type); + else if (!lit->sign) + return FALSE; /* cannot resolve on neg literal in nonneg clause */ + else /* selection ignored for negative resolution */ + return !Ordered || maximal_signed_literal(c->literals, lit, check_type); /* max pos */ + } + + else { /* ANY_RES (not necessarily positive or negative resolution) */ + if (exists_selected_literal(c->literals)) { + if (lit->sign) + return FALSE; /* if any selected lits, cannot resolve on pos lit */ + else + return selected_literal(lit); + } + else{ + /* no selected literals in clause */ + + //printf("lit = ");p_term(lit->atom); + //printf("MAX = %d ", maximal_literal(c->literals, lit, check_type)); + //printf("Ordered = %d ", !Ordered); + return !Ordered || maximal_literal(c->literals, lit, check_type); + } + } + //} } /* binary_parent_test */ /************* @@ -647,24 +688,28 @@ static void bin_res_lit(Topform giv, Literals lit, Term atom, int res_type, Lindex idx, void (*proc_proc) (Topform)) { - BOOL flipped = (lit->atom != atom); - Context nuc_subst = get_context(); - Context sat_subst = get_context(); - Term sat_atom; - Mindex_pos mate_pos; - sat_atom = mindex_retrieve_first(atom, - lit->sign ? idx->neg : idx->pos, - UNIFY, nuc_subst, sat_subst, - FALSE, &mate_pos); - while (sat_atom) { - Literals slit = atom_to_literal(sat_atom); - if (binary_parent_test(slit, res_type, FLAG_CHECK) && - check_instances(lit, nuc_subst, slit, sat_subst, res_type)) - binary_resolvent(flipped, lit, nuc_subst, slit, sat_subst, proc_proc); - sat_atom = mindex_retrieve_next(mate_pos); - } - free_context(nuc_subst); - free_context(sat_subst); + BOOL flipped = (lit->atom != atom); + Context nuc_subst = get_context(); + Context sat_subst = get_context(); + Term sat_atom; + Mindex_pos mate_pos; + sat_atom = mindex_retrieve_first(atom, + lit->sign ? idx->neg : idx->pos, + UNIFY, nuc_subst, sat_subst, + FALSE, &mate_pos); + + while (sat_atom) { + Literals slit = atom_to_literal(sat_atom); + //printf(" d1 : ");p_term(slit->atom); + if (binary_parent_test(slit, res_type, FLAG_CHECK) && + check_instances(lit, nuc_subst, slit, sat_subst, res_type)){ + //printf(" d2 : ");p_term(slit->atom); + binary_resolvent(flipped, lit, nuc_subst, slit, sat_subst, proc_proc); + } + sat_atom = mindex_retrieve_next(mate_pos); + } + free_context(nuc_subst); + free_context(sat_subst); } /* bin_res_lit */ /************* @@ -683,24 +728,29 @@ void binary_resolution(Topform c, Lindex idx, void (*proc_proc) (Topform)) { - Literals lit; - for (lit = c->literals; lit; lit = lit->next) { - if (binary_parent_test(lit, res_type, FLAG_CHECK)) { - bin_res_lit(c, lit, lit->atom, res_type, idx, proc_proc); - - /* If equality, try for resolution with the flip. */ - if (eq_term(lit->atom)) { - Term flip = top_flip(lit->atom); - bin_res_lit(c, lit, flip, res_type, idx, proc_proc); - zap_top_flip(flip); - } - - /* Try for resolution with x=x. */ - if (neg_eq(lit)) { - xx_res(lit, proc_proc); - } - } - } + Literals lit; + //printf("C : ");p_clause(c); + for (lit = c->literals; lit; lit = lit->next) { + if (binary_parent_test(lit, res_type, FLAG_CHECK)) { + bin_res_lit(c, lit, lit->atom, res_type, idx, proc_proc); + + /* If equality, try for resolution with the flip. */ + if (eq_term(lit->atom)) { + Term flip = top_flip(lit->atom); + bin_res_lit(c, lit, flip, res_type, idx, proc_proc); + zap_top_flip(flip); + } + + /* Try for resolution with x=x. */ + if (neg_eq(lit)) { + + xx_res(lit, proc_proc); + + } + } + + } + } /* binary_resolution */ /************* @@ -715,37 +765,83 @@ void binary_resolution(Topform c, /* PUBLIC */ void binary_factors(Topform c, void (*proc_proc) (Topform)) { - Literals l1; - int i = 1; - Context subst = get_context(); - for (l1 = c->literals; l1; l1 = l1->next, i++) { - Literals l2; - int j = i+1; - for (l2 = l1->next; l2; l2 = l2->next, j++) { - - Trail tr = NULL; - if (l1->sign == l2->sign && - /* maximal_literal_check ??? */ - unify(l1->atom,subst,l2->atom,subst,&tr)) { - Topform f = get_topform(); - Literals l3; - f->justification = factor_just(c, i, j); - for (l3 = c->literals; l3; l3 = l3->next) { - if (l3 != l2) - f->literals = append_literal(f->literals, apply_lit(l3, subst)); + Literals l1; + int i = 1; + Context subst = get_context(); + for (l1 = c->literals; l1; l1 = l1->next, i++) { + Literals l2; + int j = i+1; + for (l2 = l1->next; l2; l2 = l2->next, j++) { + + Trail tr = NULL; + if (l1->sign == l2->sign && + /* maximal_literal_check ??? */ + unify(l1->atom,subst,l2->atom,subst,&tr)) { + Topform f = get_topform(); + Literals l3; + f->justification = factor_just(c, i, j); + for (l3 = c->literals; l3; l3 = l3->next) { + if (l3 != l2) + f->literals = append_literal(f->literals, apply_lit(l3, subst)); + } + undo_subst(tr); + upward_clause_links(f); + f->attributes = cat_att(f->attributes, + inheritable_att_instances(c->attributes, + subst)); + (*proc_proc)(f); + } + } } - undo_subst(tr); - upward_clause_links(f); - f->attributes = cat_att(f->attributes, - inheritable_att_instances(c->attributes, - subst)); - (*proc_proc)(f); - } - } - } - free_context(subst); + free_context(subst); } /* binary_factors */ +//****************************************** Modif ********************** +/************* + * + * normalization() + * + *************/ + +/* DOCUMENTATION + */ + +/* PUBLIC */ +/*void normalization(Topform c, void (*proc_proc) (Topform)) +{ + Literals l1; + int i = 1; + Context subst = get_context(); + for (l1 = c->literals; l1; l1 = l1->next, i++) { + Literals l2; + int j = i+1; + for (l2 = l1->next; l2; l2 = l2->next, j++) { + + Trail tr = NULL; + if (l1->sign == l2->sign &&*/ + /* maximal_literal_check ??? */ + /*unify(l1->atom,subst,l2->atom,subst,&tr)) { + Topform f = get_topform(); + Literals l3; + f->justification = factor_just(c, i, j); + for (l3 = c->literals; l3; l3 = l3->next) { + if (l3 != l2) + f->literals = append_literal(f->literals, apply_lit(l3, subst)); + } + undo_subst(tr); + upward_clause_links(f); + f->attributes = cat_att(f->attributes, + inheritable_att_instances(c->attributes, + subst)); + (*proc_proc)(f); + } + } + } + free_context(subst); +}*/ /* normalization */ + +// ************************************* End Modif + /************* * * merge_literals() diff --git a/ladr/subsume.c b/ladr/subsume.c index 5d16ca0..27984dc 100644 --- a/ladr/subsume.c +++ b/ladr/subsume.c @@ -132,6 +132,7 @@ equality is not built in. /* PUBLIC */ BOOL subsumes(Topform c, Topform d) { + Context subst = get_context(); Trail tr = NULL; BOOL subsumed = subsume_literals(c->literals, subst, d, &tr); @@ -172,6 +173,51 @@ BOOL subsumes_bt(Topform c, Topform d) return rc; } /* subsumes_bt */ +//***********************Modif****************** +/* PUBLIC */ +/************* + * + * subsumes_param() + * + *************/ + +BOOL subsumes_param(Topform c, Topform d) +{ + if ((param_free(c) && !param_free(d)) || (!param_free(c) && param_free(d)) ){ + //printf("subsume_param"); + return FALSE; + } + else{ + /*printf("FF "); + p_clause(c); + p_clause(d); + printf(" FF");*/ + return subsumes(c, d); + } +} /* subsumes_param */ +/************* + * + * subsumes_param() + * + *************/ + +BOOL subsumes_bt_param(Topform c, Topform d) +{ + + if ((param_free(c) && !param_free(d)) || (!param_free(c) && param_free(d)) ){ + //printf("subsume_bt_param"); + return FALSE; + } + else{ + /*printf("FF "); + p_clause(c); + p_clause(d); + printf(" FF");*/ + return subsumes_bt(c, d); + } + + +} /* subsumes_bt_param */ /************* * * forward_subsume() @@ -184,44 +230,46 @@ BOOL subsumes_bt(Topform c, Topform d) /* PUBLIC */ Topform forward_subsume(Topform d, Lindex idx) { - Literals dlit; - Topform subsumer = NULL; - Context subst = get_context(); - int nd = number_of_literals(d->literals); - - /* We have to consider all literals of d, because when d is + Literals dlit; + Topform subsumer = NULL; + Context subst = get_context(); + int nd = number_of_literals(d->literals); + + /* We have to consider all literals of d, because when d is subsumed by c, not all literals of d have to match with a literal in c. c is indexed on the first literal only. - */ - - for (dlit=d->literals; dlit!=NULL && subsumer==NULL; dlit=dlit->next) { - Mindex mdx = dlit->sign ? idx->pos : idx->neg; - Mindex_pos pos; - Term catom = mindex_retrieve_first(dlit->atom, mdx, GENERALIZATION, - NULL, subst, FALSE, &pos); - BOOL backtrack = lindex_backtrack(idx); - while (catom != NULL && subsumer == NULL) { - Topform c = catom->container; - if (atom_number(c->literals, catom) == 1) { - int nc = number_of_literals(c->literals); - /* If c is a unit then we already know it subsumes d; otherwise, - * do a full subsumption check on the clauses. (We don't let - * a clause subsume a shorter one, because that would cause - * factors to be deleted.) */ - if (nc == 1 || (nc <= nd && (backtrack - ? subsumes_bt(c,d) - : subsumes(c,d)))) { - subsumer = c; - mindex_retrieve_cancel(pos); + + for (dlit=d->literals; dlit!=NULL && subsumer==NULL; dlit=dlit->next) { + Mindex mdx = dlit->sign ? idx->pos : idx->neg; + Mindex_pos pos; + Term catom = mindex_retrieve_first(dlit->atom, mdx, GENERALIZATION, + NULL, subst, FALSE, &pos); + BOOL backtrack = lindex_backtrack(idx); + while (catom != NULL && subsumer == NULL) { + Topform c = catom->container; + if (atom_number(c->literals, catom) == 1) { + int nc = number_of_literals(c->literals); + /* If c is a unit then we already know it subsumes d; otherwise, + * do a full subsumption check on the clauses. (We don't let + * a clause subsume a shorter one, because that would cause + * factors to be deleted.) + */ + if ((nc == 1 && param_free(d)) || (nc <= nd && (backtrack // Modif + ? subsumes_bt_param(c,d) //Modif + : subsumes_param(c,d)))) { // Modif + //printf("subsume_forward "); + //p_clause(c); + subsumer = c; + mindex_retrieve_cancel(pos); + } + } + if (subsumer == NULL) + catom = mindex_retrieve_next(pos); + } } - } - if (subsumer == NULL) - catom = mindex_retrieve_next(pos); - } - } - free_context(subst); - return subsumer; + free_context(subst); + return subsumer; } /* forward_subsume */ /************* @@ -266,8 +314,8 @@ Plist back_subsume(Topform c, Lindex idx) * a clause subsume a shorter one.) */ if (nc == 1 || (nc <= nd && (backtrack - ? subsumes_bt(c, d) - : subsumes(c, d)))) + ? subsumes_bt_param(c, d) //Modif + : subsumes_param(c, d)))) // Modif subsumees = insert_clause_into_plist(subsumees, d, FALSE); } datom = mindex_retrieve_next(pos); @@ -319,8 +367,8 @@ Topform back_subsume_one(Topform c, Lindex idx) * a clause subsume a shorter one.) */ if (nc == 1 || (nc <= nd && (backtrack - ? subsumes_bt(c, d) - : subsumes(c, d)))) { + ? subsumes_bt_param(c, d) // Modif + : subsumes_param(c, d)))) { // Modif found = TRUE; mindex_retrieve_cancel(pos); } @@ -343,35 +391,35 @@ static void atom_conflict(BOOL flipped, Topform c, BOOL sign, Term a, Lindex idx, void (*empty_proc) (Topform)) { - int n = 0; - Context subst1 = get_context(); - Context subst2 = get_context(); - Mindex mdx = sign ? idx->neg : idx->pos; - Mindex_pos pos; - Term b = mindex_retrieve_first(a, mdx, UNIFY, - subst1, subst2, FALSE, &pos); - while (b) { - Topform d = b->container; - if (number_of_literals(d->literals) == 1) { - Topform conflictor = d; - Topform empty = get_topform(); - - if (c->id == 0) - assign_clause_id(c); /* so that justification makes sense */ - c->used = TRUE; /* so it won't be discarded */ - - empty->justification = binary_res_just(c, 1, conflictor, - flipped ? -1 : 1); - inherit_attributes(c, subst1, conflictor, subst2, empty); - n++; - (*empty_proc)(empty); - b = mindex_retrieve_next(pos); - } - else - b = mindex_retrieve_next(pos); - } - free_context(subst1); - free_context(subst2); + int n = 0; + Context subst1 = get_context(); + Context subst2 = get_context(); + Mindex mdx = sign ? idx->neg : idx->pos; + Mindex_pos pos; + Term b = mindex_retrieve_first(a, mdx, UNIFY, + subst1, subst2, FALSE, &pos); + while (b) { + Topform d = b->container; + if (number_of_literals(d->literals) == 1) { + Topform conflictor = d; + Topform empty = get_topform(); + + if (c->id == 0) + assign_clause_id(c); /* so that justification makes sense */ + c->used = TRUE; /* so it won't be discarded */ + + empty->justification = binary_res_just(c, 1, conflictor, + flipped ? -1 : 1); + inherit_attributes(c, subst1, conflictor, subst2, empty); + n++; + (*empty_proc)(empty); + b = mindex_retrieve_next(pos); + } + else + b = mindex_retrieve_next(pos); + } + free_context(subst1); + free_context(subst2); } /* atom_conflict */ /************* @@ -645,49 +693,50 @@ BOOL eq_removable_literal(Topform c, Literals lit) /* PUBLIC */ void simplify_literals2(Topform c) { - Literals l; - int i; - BOOL null_literals = FALSE; - BOOL tautological = FALSE; - - if (!c->normal_vars) - renumber_variables(c, MAX_VARS); - - for (l = c->literals, i = 1; l && !tautological; l = l->next, i++) { - Term a = l->atom; - BOOL sign = l->sign; - if ((!sign && eq_term(a) && term_ident(ARG(a,0), ARG(a,1))) || - /* (!sign && true_term(a)) || */ - /* (sign && false_term(a)) || */ - eq_removable_literal(c, l)) { - /* literal is FALSE, so remove it */ - c->justification = append_just(c->justification, xx_just(i)); - zap_term(l->atom); - l->atom = NULL; - null_literals = TRUE; - } - else if ((!sign && true_term(a)) || - (sign && false_term(a))) { - zap_term(l->atom); - l->atom = NULL; - null_literals = TRUE; - } - else if ((sign && eq_term(a) && term_ident(ARG(a,0), ARG(a,1))) || - (sign && true_term(a)) || - (!sign && false_term(a))) - tautological = TRUE; - } - - if (null_literals) { - c->literals = remove_null_literals(c->literals); - c->normal_vars = 0; - renumber_variables(c, MAX_VARS); - } - - if (tautological || tautology(c->literals)) { - zap_literals(c->literals); - c->literals = new_literal(TRUE, get_rigid_term(true_sym(), 0)); - c->literals->atom->container = c; - /* justification not necessary because clause will disappear??? */ - } + Literals l; + int i; + BOOL null_literals = FALSE; + BOOL tautological = FALSE; + + if (!c->normal_vars) + renumber_variables(c, MAX_VARS); + + for (l = c->literals, i = 1; l && !tautological; l = l->next, i++) { + Term a = l->atom; + BOOL sign = l->sign; + if ((!sign && eq_term(a) && term_ident(ARG(a,0), ARG(a,1))) || + /* (!sign && true_term(a)) || */ + /* (sign && false_term(a)) || */ + eq_removable_literal(c, l)) { + /* literal is FALSE, so remove it */ + c->justification = append_just(c->justification, xx_just(i)); + zap_term(l->atom); + l->atom = NULL; + null_literals = TRUE; + } + else if ((!sign && true_term(a)) || + (sign && false_term(a))) { + zap_term(l->atom); + l->atom = NULL; + null_literals = TRUE; + } + else if ((sign && eq_term(a) && term_ident(ARG(a,0), ARG(a,1))) || + (sign && true_term(a)) || + (!sign && false_term(a))) + tautological = TRUE; + } + + if (null_literals) { + c->literals = remove_null_literals(c->literals); + c->normal_vars = 0; + renumber_variables(c, MAX_VARS); + } + + if (tautological || tautology(c->literals)) { + zap_literals(c->literals); + c->literals = new_literal(TRUE, get_rigid_term(true_sym(), 0)); + c->literals->atom->container = c; + /* justification not necessary because clause will disappear??? */ + } } /* simplify_literals2 */ + diff --git a/ladr/symbols.c b/ladr/symbols.c index d280132..3b043c3 100644 --- a/ladr/symbols.c +++ b/ladr/symbols.c @@ -49,6 +49,10 @@ static unsigned Symbol_count; /* Logic symbols when in Term form */ static char *True_sym = "$T"; +//************************ Modif*/ +static char *Succ_sym = "s"; /* "N(x)" means "alpha != x" */ +static char *Param_sym = "N"; +/************************************/ static char *False_sym = "$F"; static char *And_sym = "&"; static char *Or_sym = "|"; @@ -3004,3 +3008,33 @@ Ilist symnums_of_arity(Ilist p, int i) } } /* symnums_of_arity */ +/************************************** Modif *************************************/ +/* PUBLIC */ +/* return param symbol*/ +char *param_sym() +{ + return Param_sym; +} /* eq_sym */ +/***************************************************************************/ +static int Param_symnum = 0; +BOOL is_param_symbol(int symnum){ + if (Param_symnum == 0) { + Param_symnum = str_to_sn(param_sym(), 1); + } + return (symnum == Param_symnum ? TRUE : FALSE); +} + + +/* return succ symbol*/ +char *succ_sym() +{ + return Succ_sym; +} /* eq_sym */ +/***************************************************************************/ +static int Succ_symnum = 0; +BOOL is_succ_symbol(int symnum){ + if (Succ_symnum == 0) { + Succ_symnum = str_to_sn(succ_sym(), 1); + } + return (symnum == Succ_symnum ? TRUE : FALSE); +} \ No newline at end of file diff --git a/ladr/symbols.h b/ladr/symbols.h index df1f88a..4c9dabf 100644 --- a/ladr/symbols.h +++ b/ladr/symbols.h @@ -311,5 +311,11 @@ void process_skolem_list(Plist skolem_strings, Ilist fsyms); void process_lex_list(Plist lex_strings, Ilist syms, Symbol_type type); Ilist symnums_of_arity(Ilist p, int i); +/****************************************/ + +char *param_sym(); +BOOL is_param_symbol(int symnum); +char *succ_sym(); +BOOL is_succ_symbol(int symnum); #endif /* conditional compilation of whole file */ diff --git a/ladr/term.c b/ladr/term.c index 7ef4af2..7b5389f 100644 --- a/ladr/term.c +++ b/ladr/term.c @@ -2117,4 +2117,215 @@ Plist free_vars_term(Term t, Plist vars) } return vars; } /* free_vars_term */ +/**************************************MODIF******/ +/* DOCUMENTATION + This function checks if an atom contains \alpha */ + +/* PUBLIC */ +BOOL param_term(Term a) +{ + return is_param_symbol(SYMNUM(a)); +} /* param_term */ +/**************************************************/ +/* DOCUMENTATION + This function checks if an atom contains \alpha */ + +/* PUBLIC */ +BOOL succ_term(Term a) +{ + return is_succ_symbol(SYMNUM(a)); +} /* param_term */ +/**************************************************/ + +/* + create a term of the form s(s(s(x))) when we call shift(3,symbol_private(x)) + */ +Term shift(int J, Term x){ + if (J>0) { + return build_unary_term(str_to_sn("s", 1), shift(J-1, x)); + }else { + return x; + } +} +/* + takes a parameter term and add a shift on it + */ +Term var_term(Term a){ + + if(VARIABLE(a)){ + //int X = a->private_symbol;/*Symbol correspondant à la variable*/ + //free_term(p->args[0]); + //printf(" sisi ");p_term(shift(J, a));printf(" %d ", J); + //zap_term(a); + //a=shift(J, a); + //printf(" sisi ");p_term(a); + return a; + } + else{ + if(!CONSTANT(a)){ + //printf("c");p_term(a); + return var_term(a->args[0]); + + } + else { + fatal_error("var_term : Constant"); + } + + + } +} + +BOOL variable_term(Term a){ + + if(VARIABLE(a)){ + + return TRUE; + } + else{ + if(!CONSTANT(a)){ + //printf("c");p_term(a); + return variable_term(ARG(a, 0)); + + } + else { + return FALSE; + } + + + } +} + + + +/*........................................*/ +BOOL pureparam_cst_term(Term t){ + if (CONSTANT(t)) { + return TRUE; + + }else { + if(VARIABLE(t)) + return FALSE; + else + return pureparam_cst_term(ARG(t,0)); + } + +} + +/* DOCUMENTATION + This function checks if succ occurs in a Term t + Tests when a literal is of the form : N(t), + */ + +/* PUBLIC */ +BOOL only_succ_occurs_in(Term t) +{ + if (succ_term(t)){ + return only_succ_occurs_in(ARG(t,0)); + } + else { + if (VARIABLE(t) || CONSTANT(t)) { + return TRUE; + }else{ + return FALSE; + } + } +} /* occurs_in */ +/**/ +BOOL succ_occurs_in(Term t){ + + if (succ_term(t)) + return TRUE; + else { + if(VARIABLE(t)|| CONSTANT(t)) + return FALSE; + else{ + int i; + for (i = 0; i < ARITY(t); i++){ + if (succ_occurs_in(ARG(t,i))) + return TRUE; + } + return FALSE; + } + } +} /* succ_occurs_in */ + + +/* PUBLIC */ +/* + Check whether succ occurs once or not in t. + */ +BOOL succ_occurs_once(Term t) +{ + if (succ_term(t)) + return (VARIABLE(ARG(t,0)) || CONSTANT(ARG(t,0))); + else { + if(VARIABLE(t)|| CONSTANT(t)) + return FALSE; + else{ + int i; + for (i = 0; i < ARITY(t); i++){ + if (!succ_occurs_once(ARG(t,i))) + return FALSE; + } + return FALSE; + } + } +} /* occurs_in */ +/* + Check whether succ occurs once or less in t. + */ +BOOL regular_term(Term t) +{ + if (succ_term(t)) + return (VARIABLE(ARG(t,0)) || CONSTANT(ARG(t,0))); + else { + if(VARIABLE(t)|| CONSTANT(t)) + return TRUE; + else{ + int i; + for (i = 0; i < ARITY(t); i++){ + if (!regular_term(ARG(t,i))) + return FALSE; + } + return TRUE; + } + } +} /* occurs_in */ + +/************* + * + * fprint_term(fp, t) + * + *************/ + +/* DOCUMENTATION + This routine prints (to FILE *fp) a term . A newline is NOT printed. + the usual operation such as multiplication are printed infixed + */ + +/* PUBLIC */ +void fprint_term_infix(FILE *fp, Term t) +{ + if (t == NULL) + fprintf(fp, "fprint_term: NULL term\n"); + else { + if (VARIABLE(t)) + fprintf(fp, "v%d", VARNUM(t)); + else { + fprint_sym(fp, SYMNUM(t)); + + if (COMPLEX(t)) { + int i; + fprintf(fp, "("); + for (i = 0; i < ARITY(t); i++) { + fprint_term(fp, ARG(t,i)); + if (i < ARITY(t)-1) + fprintf(fp, ","); + } + fprintf(fp, ")"); + } + } + } + fflush(fp); +} /* fprint_term_infix */ diff --git a/ladr/term.h b/ladr/term.h index bd2fbb9..2bbc807 100644 --- a/ladr/term.h +++ b/ladr/term.h @@ -279,5 +279,27 @@ BOOL tlist_subset(Plist a, Plist b); BOOL tlist_set(Plist a); Plist free_vars_term(Term t, Plist vars); +/**************************************************/ +BOOL param_term(Term a); + +BOOL succ_term(Term a); + +Term shift(int J, Term x); + +Term var_term(Term a); + +BOOL variable_term(Term a); + +BOOL pureparam_cst_term(Term t); + +BOOL only_succ_occurs_in(Term t); + +BOOL succ_occurs_in(Term t); + +BOOL succ_occurs_once(Term t); + +BOOL regular_term(Term t); + +void fprint_term_infix(FILE *fp, Term t); #endif /* conditional compilation of whole file */ diff --git a/ladr/termorder.c b/ladr/termorder.c index 07f0196..0bc8148 100644 --- a/ladr/termorder.c +++ b/ladr/termorder.c @@ -366,7 +366,20 @@ BOOL lrpo(Term s, Term t, BOOL lex_order_vars) else return occurs_in(t, s); /* s > var iff s properly contains that var */ } - + /***********************Modif ***********/ + /* else if(succ_occurs_in(s) && !succ_occurs_in(t)){ + //printf("t1 "); p_term(alpha);printf("t1 "); + //printf("t2 "); p_term(beta); printf("t2 "); + return TRUE; + } + else if(!succ_occurs_in(s) && succ_occurs_in(t)){ + //printf("k1 "); p_term(alpha);printf("k1 "); + //printf("k2 "); p_term(beta); printf("k2 "); + + return FALSE; + }*/ + + /*................... End Modif.....................*/ else if (SYMNUM(s) == SYMNUM(t) && sn_to_lrpo_status(SYMNUM(s)) == LRPO_LR_STATUS) /* both have the same "left-to-right" symbol. */ @@ -412,33 +425,33 @@ Symbols are written as constants; arity is deduced from the symbol table. /* PUBLIC */ void init_kbo_weights(Plist weights) { - Plist p; - for (p = weights; p; p = p->next) { - Term t = p->v; - if (!is_eq_symbol(SYMNUM(t))) - fatal_error("init_kbo_weights, not equality"); - else { - Term a = ARG(t,0); - Term b = ARG(t,1); - if (!CONSTANT(a)) - fatal_error("init_kbo_weights, symbol not constant"); - else { - int wt = natural_constant_term(b); - if (wt == -1) - fatal_error("init_kbo_weights, weight not natural"); - else { - char *str = sn_to_str(SYMNUM(a)); - int symnum = function_or_relation_sn(str); - if (symnum == -1) { - char mess[200]; - sprintf(mess, "init_kbo_weights, symbol %s not found", str); - fatal_error(mess); - } - set_kb_weight(symnum, wt); + Plist p; + for (p = weights; p; p = p->next) { + Term t = p->v; + if (!is_eq_symbol(SYMNUM(t))) + fatal_error("init_kbo_weights, not equality"); + else { + Term a = ARG(t,0); + Term b = ARG(t,1); + if (!CONSTANT(a)) + fatal_error("init_kbo_weights, symbol not constant"); + else { + int wt = natural_constant_term(b); + if (wt == -1) + fatal_error("init_kbo_weights, weight not natural"); + else { + char *str = sn_to_str(SYMNUM(a)); + int symnum = function_or_relation_sn(str); + if (symnum == -1) { + char mess[200]; + sprintf(mess, "init_kbo_weights, symbol %s not found", str); + fatal_error(mess); + } + set_kb_weight(symnum, wt); + } + } + } } - } - } - } } /* init_kbo_weights */ /************* @@ -476,50 +489,65 @@ Is alpha kbo-greater-than beta? /* PUBLIC */ BOOL kbo(Term alpha, Term beta, BOOL lex_order_vars) -{ - if (VARIABLE(alpha)) { - if (lex_order_vars) - return VARIABLE(beta) && VARNUM(alpha) > VARNUM(beta); - else - return FALSE; - } - else if (VARIABLE(beta)) { - if (lex_order_vars) - return TRUE; - else - return occurs_in(beta, alpha); - } - else if (ARITY(alpha) == 1 && ARITY(beta) == 1 && - SYMNUM(alpha) == SYMNUM(beta)) - return kbo(ARG(alpha, 0), ARG(beta, 0), lex_order_vars); - else if (!variables_multisubset(beta, alpha)) - return FALSE; - else { - int wa = kbo_weight(alpha); - int wb = kbo_weight(beta); - /* printf("kbo_weight=%d: ", wa); p_term(alpha); */ - /* printf("kbo_weight=%d: ", wb); p_term(beta); */ - if (wa > wb) - return TRUE; - else if (wa < wb) - return FALSE; - else if (!variables_multisubset(alpha, beta)) - return FALSE; /* if weights same, multisets of variables must be same */ - else if (sym_precedence(SYMNUM(alpha), SYMNUM(beta)) == GREATER_THAN) - return TRUE; - else if (SYMNUM(alpha) != SYMNUM(beta)) - return FALSE; - else { - /* Call KBO on first arguments that differ. */ - int i = 0; - while (i < ARITY(alpha) && term_ident(ARG(alpha,i),ARG(beta,i))) - i++; - if (i == ARITY(alpha)) - return FALSE; - else - return kbo(ARG(alpha,i), ARG(beta,i), lex_order_vars); - } - } +{ + + if (VARIABLE(alpha)) { + if (lex_order_vars) + return VARIABLE(beta) && VARNUM(alpha) > VARNUM(beta); + else + return FALSE; + } + else if (VARIABLE(beta)) { + if (lex_order_vars) + return TRUE; + else + return occurs_in(beta, alpha); + } + /***********************Modif ***********/ + else if(succ_occurs_in(alpha) && !succ_occurs_in(beta)){ + // printf("t1 "); p_term(alpha);printf("t1 "); + // printf("t2 "); p_term(beta); printf("t2 "); + return TRUE; + } + else if(!succ_occurs_in(alpha) && succ_occurs_in(beta)){ + // printf("k1 "); p_term(alpha);printf("k1 "); + // printf("k2 "); p_term(beta); printf("k2 "); + + return FALSE; + } + + /*................... End Modif.....................*/ + else if (ARITY(alpha) == 1 && ARITY(beta) == 1 && + SYMNUM(alpha) == SYMNUM(beta)) + return kbo(ARG(alpha, 0), ARG(beta, 0), lex_order_vars); + else if (!variables_multisubset(beta, alpha)) + return FALSE; + else { + int wa = kbo_weight(alpha); + int wb = kbo_weight(beta); + //printf("kbo_weight=%d: ", wa); p_term(alpha); + //printf("kbo_weight=%d: ", wb); p_term(beta); + if (wa > wb) + return TRUE; + else if (wa < wb) + return FALSE; + else if (!variables_multisubset(alpha, beta)) + return FALSE; /* if weights same, multisets of variables must be same */ + else if (sym_precedence(SYMNUM(alpha), SYMNUM(beta)) == GREATER_THAN) + return TRUE; + else if (SYMNUM(alpha) != SYMNUM(beta)) + return FALSE; + else { + /* Call KBO on first arguments that differ. */ + int i = 0; + while (i < ARITY(alpha) && term_ident(ARG(alpha,i),ARG(beta,i))) + i++; + if (i == ARITY(alpha)) + return FALSE; + else + return kbo(ARG(alpha,i), ARG(beta,i), lex_order_vars); + } + } } /* kbo */ /************* @@ -535,10 +563,14 @@ Is alpha > beta in the current term ordering? (LPR, RPO, KBO) /* PUBLIC */ BOOL term_greater(Term alpha, Term beta, BOOL lex_order_vars) { - if (Ordering_method == KBO_METHOD) + //printf("t1 ");p_term(alpha);p_term(beta);printf("\n t1 "); + if (Ordering_method == KBO_METHOD){ + return kbo(alpha, beta, lex_order_vars); - else + } + else{ return lrpo(alpha, beta, lex_order_vars); /* LPO, RPO, LRPO */ + } } /* term_greater */ /************* @@ -555,6 +587,7 @@ Return GREATER_THAN, LESS_THAN, SAME_AS, or NOT_COMPARABLE. /* PUBLIC */ Ordertype term_order(Term alpha, Term beta) { + if (term_greater(alpha, beta, FALSE)) return GREATER_THAN; else if (term_greater(beta, alpha, FALSE)) diff --git a/ladr/top_input.c b/ladr/top_input.c index 815e398..4829672 100644 --- a/ladr/top_input.c +++ b/ladr/top_input.c @@ -362,7 +362,7 @@ void flag_handler(FILE *fout, Term t, BOOL echo, int unknown_action) { int flag = str_to_flag_id(sn_to_str(SYMNUM(ARG(t,0)))); if (flag == -1) - execute_unknown_action(fout, unknown_action, t, "Flag not recognized"); + execute_unknown_action(fout, unknown_action, t, "Flag not recognized1"); else { update_flag(fout, flag, is_term(t, "set", 1), echo); if (is_term(ARG(t,0), "arithmetic", 0)) { diff --git a/ladr/topform.c b/ladr/topform.c index b6d31a5..038c769 100644 --- a/ladr/topform.c +++ b/ladr/topform.c @@ -1,4 +1,4 @@ -/* Copyright (C) 2006, 2007 William McCune + /* Copyright (C) 2006, 2007 William McCune This file is part of the LADR Deduction Library. @@ -18,8 +18,7 @@ #include "topform.h" -/* Private definitions and types */ - +/* Private definitions and types /* * memory management */ @@ -40,6 +39,8 @@ static unsigned Topform_gets, Topform_frees; Topform get_topform(void) { Topform p = get_cmem(PTRS_TOPFORM); + init_ancestors_topform(p); + //p->ancestors= NULL; Topform_gets++; return(p); } /* get_topform */ @@ -142,32 +143,33 @@ This routine prints a clause to a file. /* PUBLIC */ void fprint_clause(FILE *fp, Topform c) { - if (c == NULL) - fprintf(fp, "fprint_clause: NULL clause\n"); - else { - Literals lit; - - if (c->id > 0) - fprintf(fp, "%d: ", c->id); - - if (c->literals == NULL) - fprintf(fp, "%s", false_sym()); - else { - for (lit = c->literals; lit != NULL; lit = lit->next) { - if (!lit->sign) - fprintf(fp, "%s", not_sym()); - fprint_term(fp, lit->atom); + + if (c == NULL) + fprintf(fp, "fprint_clause: NULL clause\n"); + else { + Literals lit; + + if (c->id > 0){ + fprintf(fp, "%d: ", c->id); + } + if (c->literals == NULL) + fprintf(fp, "%s", false_sym()); + else { + for (lit = c->literals; lit != NULL; lit = lit->next) { + if (!lit->sign) + fprintf(fp, "%s", not_sym()); + fprint_term(fp, lit->atom); #if 0 - if (maximal_literal_check(lit)) - fprintf(fp, "[max]"); + if (maximal_literal_check(lit)) + fprintf(fp, "[max]"); #endif - if (lit->next != NULL) - fprintf(fp, " %s ", or_sym()); - } - } - fprintf(fp, ".\n"); - } - fflush(fp); + if (lit->next != NULL) + fprintf(fp, " %s ", or_sym()); + } + } + fprintf(fp, ".\n"); + } + fflush(fp); } /* fprint_clause */ /************* @@ -757,9 +759,9 @@ before starting search)/ */ /* PUBLIC */ -BOOL initial_clause(Topform c) +BOOL initial_clause(Topform p) { - return c->initial; + return p->initial; } /* initial_clause */ /************* @@ -893,4 +895,483 @@ Ordertype cl_wt_id_compare(Topform c1, Topform c2) else return SAME_AS; } /* cl_wt_id_compare */ +/************************************* Modif *********************************************/ + +/* DOCUMENTATION + */ + +/* ****************** + * + * get_rank() + * + *********************/ + +int get_rank(Topform p){ + return p->rank; + +} /*get_rank */ + +/* ****************** + * + * compute_rank() + * + *********************/ +/* Compute the rank of a clause + */ +int compute_rank(Topform p){ + int depth_param =0; + int max_depth = 0; + BOOL N=FALSE; + //printf("couoooooooooooooooooo"); + + if (param_free(p)) { + + return -1; + } + else{ + Literals lit; + Term t; + //printf("couoooooooooooooooooo"); + for(lit = p->literals; lit != NULL; lit = lit->next){ + + t = lit->atom; + if (param_term(t)){ + depth_param = term_depth(t); + + } + else{ + if (succ_occurs_in(t)){// if "s" occurs once + + max_depth = 1; + } + } + + } + + + + //printf(" max_depth = %d ", max_depth); + //p_clause(p); + //printf("depth_param = %d ", depth_param); + return depth_param - max_depth - 1 ; + } +} +/* + check wether the para term is not a constant + */ +BOOL not_const_param(Topform c){ + Literals lit; + Term t; + //BOOL B = TRUE; + for (lit = c->literals; lit != NULL; lit = lit->next){ + t = lit->atom; + + if (param_term(t)){ + //B=TRUE; + if(variable_term(t)){ + return TRUE; + } + } + + } + + return FALSE; +} +/*Initialize the rank and the var_term*/ +void init_rank(Topform p){ + p->rank=compute_rank(p); + p->var_term = not_const_param(p); +} +BOOL get_var_term(Topform c){ + return c->var_term; +} + +/* Retourne vrai si la clause n'a pas de parametre \alpha */ +BOOL param_free(Topform p){ + Term t; + Literals lit; + if (p==NULL) { + return TRUE; + } + + for (lit = p->literals; lit != NULL; lit = lit->next){ + t = lit->atom; + if (param_term(t)) { + return FALSE; + } + } + return TRUE; +} + +/*********************/ +/* Retourne le nombre d'occurence du parametre*/ +int param_occurrences(Topform p){ + Literals lit; + Term t; + int num = 0; + for (lit = p->literals; lit != NULL; lit = lit->next){ + t = lit->atom; + if (param_term(t)) num++; + } + return num; +} +/* retourne vrai si la clause est normalisée */ +BOOL is_normalized(Topform p){ + return (param_occurrences(p) < 2) ; + +} + + +/********************* + print_ancestors(Topform) +**********************/ +void print_ancestors(Topform p){ + p_ilist(p->ancestors); +} +/**********************/ +void init_ancestors_topform(Topform p){ + p->ancestors = get_ilist(); +} + +/*................................*/ +BOOL bottom_clause(Topform p){ + return p->rank == -1; +} +/*...................................*/ +/* + retourne shift(clause, J) + */ +Topform shift_cl(Topform p, int J){ + + Topform c = copy_clause(p); + if(param_free(p)){ + return c; + } + Term t; + int i =0; + Literals lit; + int rank=get_rank(p); + if (rank==NULL) { + init_rank(p); + rank = get_rank(p); + } + for (lit = c->literals; lit != NULL; lit = lit->next){ + t = lit->atom; + //printf("i = %d ", i); + //p_term(t); + if (param_term(t)){ + + if(variable_term(t)){ + //int depth=term_depth(t); + int j = J-rank; + Term x= var_term(t);// save the index variable + Term sx=shift(j, x);/* build the shift term with the index variable + of the form s^j(x)*/ + //printf("J = %d ",j); + //printf("shift_term ");p_term(sx);printf("..\n"); + lit->atom = subst_term(t, x, sx); // build the entire parameter shifted term of the form : + // N(s^j(x) + //printf("shift_cl ");p_term(lit->atom);printf("..\n"); + lit->sign= TRUE; + c->rank = J; + upward_term_links(t, p); + } + + + + + + + } + i++; + + } + //p_clause(c); +return c; + +} +/*......................................*/ +/* + renvoie une vrai si c'est une clause de la forme N(s^i(CST)) + */ +BOOL pureparam_cst_topform(Topform p){ + if(number_of_literals(p->literals)==1){ + if (param_term(p->literals->atom)) { + return pureparam_cst_term(p->literals->atom); + } + else { + return FALSE; + } + + }else{ + return FALSE; + } + +} + + + +/* + return the clause without param literal + */ +Topform topform_without_param(Topform c){ + //printf("huu"); + if (!param_free(c)) { + + Topform c1 = copy_clause(c); + c1->literals=remove_param_literals(c1->literals); + return c1; + } + else{ + + return c; + } +} +/*...........................................*/ +/* + Return true if p1 et p1 are identical with literals not ordered in the same way i.e clause_ident fails + */ +BOOL clause_ident_order(Topform p1, Topform p2){ + //printf("lits1 %d ", count_literal(p1->literals)); + //printf("lits2 %d ", count_literal(p2->literals)); + if(count_literal(p1->literals) == count_literal(p2->literals)){ + //printf("literal_ident = %d \n", literals_ident(p1->literals, p2->literals)); + return literals_ident(p1->literals, p2->literals); + }else { + + return FALSE; + } +} +/* + return true if the clause is of the form N(s^i(x)) i.e n < i. + */ +BOOL loop_clause(Topform p){ + return loop_literals(p->literals); +} +/**/ +BOOL alpha_C_clause(Topform c){ + + Literals lit; + Term t; + for (lit = c->literals; lit != NULL; lit = lit->next){ + t = lit->atom; + if (param_term(t)) { + if(!only_succ_occurs_in(ARG(t,0)) ){ + //printf("term prob ="); + //p_term(t); + return FALSE; + } + } + else { + if(!regular_term(t)){ + //printf("term prob ="); + //p_term(t); + return FALSE; + } + } + + } + return TRUE; +} +/***************************************build_loop_clause()***************/ + +Topform build_loop_clause(Topform p){ + Topform c = copy_clause_with_flags(p); + + c->rank = p->rank - 1; + Term t; + Literals lit; + for (lit = c->literals; lit != NULL; lit = lit->next){ + t = lit->atom; + //printf("i = %d ", i); + p_term(t); + if (param_term(t)){ + + if(variable_term(t)){ + //int depth=term_depth(t); + + Term x= var_term(t);// save the index variable + Term sx=shift(1, x);/* build the shift term with the index variable + of the form s^j(x)*/ + //printf("J = %d ",j); + //printf("shift_term ");p_term(sx);printf("..\n"); + Term Nsx = subst_term(t, x, sx); // build the entire parameter shifted term of the form : + + // N(s^j(x) + printf("shift_cl ");p_term(Nsx);printf("..\n"); + + lit->atom = Nsx; + //printf(" res "); p_clause(res); + + } + + + + + + } + + } + p_clause(c); + return c; +} + +/************* + * + * cl_rank_compare() + * + *************/ + +/* DOCUMENTATION + */ + +Ordertype cl_rank_compare2(Topform c1, Topform c2) +{ + if (c1->rank == NULL) { + init_rank(c1); + } + if (c2->rank == NULL) { + init_rank(c2); + } + if (c1->id == 117) { + printf("F "); + p_clause(c2); + printf(" F "); + + } + if (c1->rank != -1 && c2->rank != -1) { + + if (c1->rank < c2->rank ) + return LESS_THAN; + else if (c1->rank > c2->rank) + return GREATER_THAN; + else if (c1->id < c2->id) + return LESS_THAN; + else if (c1->id > c2->id) + return GREATER_THAN; + else + return SAME_AS; + + } + else if (c1->id < c2->id) + return LESS_THAN; + else if (c1->id > c2->id) + return GREATER_THAN; + else + return SAME_AS; + + + + +} +// Return +Ordertype cl_rank_compare(Topform c1, Topform c2) +{ + if (c1->rank == NULL) { + init_rank(c1); + } + if (c2->rank == NULL) { + init_rank(c2); + } + if (c1->rank < c2->rank) + return LESS_THAN; + else if (c1->rank > c2->rank) + return GREATER_THAN; + else if (c1->id < c2->id) + return LESS_THAN; + else if (c1->id > c2->id) + return GREATER_THAN; + else + return SAME_AS; + + + + +} + +/************* + * + * fprint_clause_param() + * + *************/ + +/* DOCUMENTATION + This routine prints a clause to a file. + */ +/* PUBLIC */ +void fprint_clause_param(FILE *fp, Topform c) +{ + Term param; + int n_literals = 0; + if (c == NULL) + fprintf(fp, "fprint_clause: NULL clause\n"); + else { + Literals lit; + + if (c->id > 0){ + fprintf(fp, "%d: ", c->id); + } + if (c->literals == NULL) + fprintf(fp, "%s", false_sym()); + else { + fprintf(fp, " [ "); + for (lit = c->literals; lit != NULL; lit = lit->next) { + n_literals++; + if (param_term(lit->atom)) { + param = lit->atom; + if (lit->next != NULL && n_literals > 1) + fprintf(fp, " %s ", or_sym()); + } + else{ + if (eq_term(lit->atom)) { + fprint_term_infix(fp, ARG(lit->atom,0)); + if (!lit->sign) + fprintf(fp, " != "); + else + fprintf(fp, " = "); + + fprint_term_infix(fp, ARG(lit->atom,1)); + if (lit->next != NULL && !param_term(lit->next->atom)) + fprintf(fp, " %s ", or_sym()); + } + else{ + if (!lit->sign) + fprintf(fp, "%s", not_sym()); + + fprint_term_infix(fp, lit->atom); +#if 0 + if (maximal_literal_check(lit)) + fprintf(fp, "[max]"); +#endif + if (lit->next != NULL && !param_term(lit->next->atom)) + fprintf(fp, " %s ", or_sym()); + } + } + } + } + if (n_literals > 1) { + fprintf(fp, " if "); + } + fprintf(fp, " n = "); + fprint_term(fp, ARG(param,0)); + fprintf(fp, " ].\n"); + } + fflush(fp); +} /* fprint_clause */ + +/************* + * + * p_clause_param() + * + *************/ + +/* DOCUMENTATION + This routine prints a clause to stdout. + */ + +/* PUBLIC */ +void p_clause_param(Topform c) +{ + fprint_clause_param(stdout, c); +} /* p_clause */ \ No newline at end of file diff --git a/ladr/topform.h b/ladr/topform.h index b8058b6..ca9d87f 100644 --- a/ladr/topform.h +++ b/ladr/topform.h @@ -69,7 +69,7 @@ struct topform { /* for formulas only */ Formula formula; - + int semantics; /* evaluation in interpretations */ /* The rest of the fields are flags. These could be bits. */ @@ -81,6 +81,10 @@ struct topform { char initial; /* existed at the start of the search */ char neg_compressed; /* negative and compressed */ char subsumer; /* has this clause back subsumed anything? */ + + int rank; /* the level of the clause */ + BOOL var_term; + Ilist ancestors; }; @@ -152,4 +156,44 @@ Ordertype cl_id_compare(Topform c1, Topform c2); Ordertype cl_wt_id_compare(Topform c1, Topform c2); +/*********************************************************************/ +void init_rank(Topform p); + +int get_rank(Topform p); + +int compute_rank(Topform p); + +BOOL param_free(Topform p); + +//void add_ancestors(Topform p1, Topform p2, Topform p); + +void print_ancestors(Topform p); + +BOOL bottom_clause(Topform p); + +Topform shift_cl(Topform p, int J); + +BOOL pureparam_cst_topform(Topform p); + +Topform topform_without_param(Topform c); + +BOOL clause_ident_order(Topform p1, Topform p2); + +BOOL loop_clause(Topform p); + +BOOL not_const_param(Topform c); + +BOOL get_var_term(Topform c); + +BOOL alpha_C_clause(Topform c); + +Topform build_loop_clause(Topform p); + +//order by rank + +Ordertype cl_rank_compare(Topform c1, Topform c2); + +void fprint_clause_param(FILE *fp, Topform c); + +void p_clause_param(Topform c); #endif /* conditional compilation of whole file */ diff --git a/ladr/unify.c b/ladr/unify.c index 40f586e..586517a 100644 --- a/ladr/unify.c +++ b/ladr/unify.c @@ -238,6 +238,7 @@ context c1 is different from variable v1 in context c2.) */ /* PUBLIC */ +/* Ajouter si param()*/ BOOL unify(Term t1, Context c1, Term t2, Context c2, Trail *trp) { diff --git a/provers.src/Makefile b/provers.src/Makefile index 78c2543..2913243 100644 --- a/provers.src/Makefile +++ b/provers.src/Makefile @@ -17,7 +17,8 @@ PRVR_OBJ = index_lits.o forward_subsume.o demodulate.o\ search.o\ utilities.o\ provers.o\ - foffer.o + foffer.o\ + loop.o OBJECTS = $(PRVR_OBJ) @@ -114,10 +115,11 @@ white_black.o: white_black.h search-structures.h actions.o: actions.h search-structures.h +loop.o: loop.h ../ladr/literals.h ../ladr/attrib.h ../ladr/formula.h ../ladr/maximal.h search.o: search.h search-structures.h semantics.h pred_elim.h demodulate.h index_lits.h forward_subsume.h unfold.h actions.h giv_select.h white_black.h utilities.h ../ladr/interp.h ../ladr/ioutil.h ../ladr/subsume.h ../ladr/resolve.h ../ladr/clauses.h ../ladr/clause_misc.h ../ladr/ioutil.h ../ladr/ladr.h ../ladr/clock.h ../ladr/subsume.h ../ladr/di_tree.h ../ladr/subsume.h ../ladr/clock.h ../ladr/parautil.h ../ladr/clist.h ../ladr/ioutil.h utilities.o: utilities.h search-structures.h -provers.o: provers.h search.h search-structures.h semantics.h pred_elim.h demodulate.h index_lits.h forward_subsume.h unfold.h actions.h giv_select.h white_black.h utilities.h ../ladr/interp.h ../ladr/ioutil.h ../ladr/subsume.h ../ladr/resolve.h ../ladr/clauses.h ../ladr/clause_misc.h ../ladr/ioutil.h ../ladr/ladr.h ../ladr/clock.h ../ladr/subsume.h ../ladr/di_tree.h ../ladr/subsume.h ../ladr/clock.h ../ladr/parautil.h ../ladr/clist.h ../ladr/ioutil.h +provers.o: provers.h search.h search-structures.h semantics.h pred_elim.h demodulate.h index_lits.h forward_subsume.h unfold.h actions.h giv_select.h white_black.h utilities.h loop.h ../ladr/interp.h ../ladr/ioutil.h ../ladr/subsume.h ../ladr/resolve.h ../ladr/clauses.h ../ladr/clause_misc.h ../ladr/ioutil.h ../ladr/ladr.h ../ladr/clock.h ../ladr/subsume.h ../ladr/di_tree.h ../ladr/subsume.h ../ladr/clock.h ../ladr/parautil.h ../ladr/clist.h ../ladr/ioutil.h -foffer.o: foffer.h search.h search-structures.h semantics.h pred_elim.h demodulate.h index_lits.h forward_subsume.h unfold.h actions.h giv_select.h white_black.h utilities.h ../ladr/interp.h ../ladr/ioutil.h ../ladr/subsume.h ../ladr/resolve.h ../ladr/clauses.h ../ladr/clause_misc.h ../ladr/ioutil.h ../ladr/ladr.h ../ladr/clock.h ../ladr/subsume.h ../ladr/di_tree.h ../ladr/subsume.h ../ladr/clock.h ../ladr/parautil.h ../ladr/clist.h ../ladr/ioutil.h +foffer.o: foffer.h search.h search-structures.h semantics.h pred_elim.h demodulate.h index_lits.h forward_subsume.h unfold.h actions.h giv_select.h loop.h white_black.h utilities.h ../ladr/interp.h ../ladr/ioutil.h ../ladr/subsume.h ../ladr/resolve.h ../ladr/clauses.h ../ladr/clause_misc.h ../ladr/ioutil.h ../ladr/ladr.h ../ladr/clock.h ../ladr/subsume.h ../ladr/di_tree.h ../ladr/subsume.h ../ladr/clock.h ../ladr/parautil.h ../ladr/clist.h ../ladr/ioutil.h diff --git a/provers.src/giv_select.c b/provers.src/giv_select.c index 29c96c3..a1bf5b4 100644 --- a/provers.src/giv_select.c +++ b/provers.src/giv_select.c @@ -25,7 +25,8 @@ enum { GS_ORDER_WEIGHT, GS_ORDER_AGE, - GS_ORDER_RANDOM + GS_ORDER_RANDOM, + GS_ORDER_RANK }; /* order */ typedef struct giv_select *Giv_select; @@ -121,65 +122,77 @@ int current_cycle_size(Select_state s) *************/ /* DOCUMENTATION + Initialize */ /* PUBLIC */ void init_giv_select(Plist rules) { - Plist p; - - for (p = rules; p; p = p->next) { - Term t = p->v; - int n = 0; - Term order_term; - Term property_term; - Giv_select gs; - if (!is_term(t, "=", 2) || - !is_term(ARG(t,0), "part", 4) || - !CONSTANT(ARG(ARG(t,0),0)) || - !(is_constant(ARG(ARG(t,0),1), "high") || - is_constant(ARG(ARG(t,0),1), "low")) || - !((n = natural_constant_term(ARG(t,1))) > 0)) - fatal_error("Given selection rule must be: " - "part(,high|low,age|wt|random,)="); - - order_term = ARG(ARG(t,0),2); - property_term = ARG(ARG(t,0),3); - gs = get_giv_select(); - - if (is_constant(ARG(ARG(t,0),1), "high")) { - High.selectors = plist_append(High.selectors, gs); - High.cycle_size += n; - } - else { - Low.selectors = plist_append(Low.selectors, gs); - Low.cycle_size += n; - } - - gs->name = term_symbol(ARG(ARG(t,0),0)); - gs->part = n; - if (is_constant(order_term,"weight")) { - gs->order = GS_ORDER_WEIGHT; - gs->compare = (Ordertype (*) (void *, void *)) cl_wt_id_compare; - } - else if (is_constant(order_term,"age")) { - gs->order = GS_ORDER_AGE; - gs->compare = (Ordertype (*) (void *, void *)) cl_id_compare; - } - else if (is_constant(order_term,"random")) { - gs->order = GS_ORDER_RANDOM; - gs->compare = (Ordertype (*) (void *, void *)) cl_id_compare; - } - else - fatal_error("Given selection order must be weight, age, or random."); - gs->property = compile_clause_eval_rule(property_term); - if (gs->property == NULL) - fatal_error("Error in clause-property expression of given selection rule"); - else if (rule_contains_semantics(gs->property)) - Rule_needs_semantics = TRUE; - } - High.current = High.selectors; - Low.current = Low.selectors; + Plist p; + + for (p = rules; p; p = p->next) { + Term t = p->v; + int n = 0; + Term order_term; + Term property_term; + Giv_select gs; + if (!is_term(t, "=", 2) || + !is_term(ARG(t,0), "part", 4) || + !CONSTANT(ARG(ARG(t,0),0)) || + !(is_constant(ARG(ARG(t,0),1), "high") || + is_constant(ARG(ARG(t,0),1), "low")) || + !((n = natural_constant_term(ARG(t,1))) > 0)) + fatal_error("Given selection rule must be: " + "part(,high|low,age|wt|random,)="); + + order_term = ARG(ARG(t,0),2); + property_term = ARG(ARG(t,0),3); + gs = get_giv_select(); + + if (is_constant(ARG(ARG(t,0),1), "high")) { + High.selectors = plist_append(High.selectors, gs); + High.cycle_size += n; + } + else { + Low.selectors = plist_append(Low.selectors, gs); + Low.cycle_size += n; + } + + gs->name = term_symbol(ARG(ARG(t,0),0)); + gs->part = n; + if (is_constant(order_term,"weight")) { + gs->order = GS_ORDER_WEIGHT; + printf("W"); + gs->compare = (Ordertype (*) (void *, void *)) cl_wt_id_compare; + } + else if (is_constant(order_term,"age")) { + gs->order = GS_ORDER_AGE; + + gs->compare = (Ordertype (*) (void *, void *)) cl_id_compare; + } + else if (is_constant(order_term,"random")) { + gs->order = GS_ORDER_RANDOM; + gs->compare = (Ordertype (*) (void *, void *)) cl_id_compare; + //Modif + + } + //********* Modif + else if (is_constant(order_term,"rank")) { + gs->order = GS_ORDER_RANK; + + gs->compare = (Ordertype (*) (void *, void *)) cl_rank_compare; // cl_rank_compare sorts a list of topform by rank + } + //******* End Modif + else + fatal_error("Given selection order must be weight, age, or random."); + gs->property = compile_clause_eval_rule(property_term); + if (gs->property == NULL) + fatal_error("Error in clause-property expression of given selection rule"); + else if (rule_contains_semantics(gs->property)) + Rule_needs_semantics = TRUE; + } + High.current = High.selectors; + Low.current = Low.selectors; } /* init_giv_select */ /************* @@ -191,54 +204,155 @@ void init_giv_select(Plist rules) static void update_selectors(Topform c, BOOL insert) { - BOOL matched = FALSE; - Plist p; - for (p = High.selectors; p; p = p->next) { - Giv_select gs = p->v; - if (eval_clause_in_rule(c, gs->property)) { - matched = TRUE; - if (insert) { - gs->idx = avl_insert(gs->idx, c, gs->compare); - High.occurrences++; - } - else { - gs->idx = avl_delete(gs->idx, c, gs->compare); - High.occurrences--; - } - } - } - /* If it is high-priority, don't let it also be low priority. */ - if (!matched) { - for (p = Low.selectors; p; p = p->next) { - Giv_select gs = p->v; - if (eval_clause_in_rule(c, gs->property)) { - matched = TRUE; - if (insert) { - gs->idx = avl_insert(gs->idx, c, gs->compare); - Low.occurrences++; + BOOL matched = FALSE; + Plist p; + for (p = High.selectors; p; p = p->next) { + Giv_select gs = p->v; + if (eval_clause_in_rule(c, gs->property)) { + matched = TRUE; + if (insert) { + //Modif + //printf(" insert "); + //p_clause(c); + gs->idx = avl_insert(gs->idx, c, gs->compare); + High.occurrences++; + } + else { + //Modif + //printf(" yeah3 "); + //p_clause(c); + + gs->idx = avl_delete(gs->idx, c, gs->compare); + High.occurrences--; + } + } } - else { - gs->idx = avl_delete(gs->idx, c, gs->compare); - Low.occurrences--; + /* If it is high-priority, don't let it also be low priority. */ + if (!matched) { + for (p = Low.selectors; p; p = p->next) { + Giv_select gs = p->v; + if (eval_clause_in_rule(c, gs->property)) { + matched = TRUE; + if (insert) { + //Modif + //printf(" insert2 "); + //p_clause(c); + + gs->idx = avl_insert(gs->idx, c, gs->compare); + Low.occurrences++; + } + else { + //Modif + //printf("yeah2"); + //p_clause(c); + + gs->idx = avl_delete(gs->idx, c, gs->compare); + Low.occurrences--; + } + } + } + } + if (!matched) { + static BOOL Already_warned = FALSE; + + if (!Already_warned) { + fprintf(stderr, "\n\nWARNING: one or more kept clauses do not match " + "any given_selection rules (see output).\n\n"); + printf("\nWARNING: the following clause does not match " + "any given_selection rules.\n" + "This message will not be repeated.\n"); + f_clause(c); + Already_warned = TRUE; + } } - } - } - } - if (!matched) { - static BOOL Already_warned = FALSE; - - if (!Already_warned) { - fprintf(stderr, "\n\nWARNING: one or more kept clauses do not match " - "any given_selection rules (see output).\n\n"); - printf("\nWARNING: the following clause does not match " - "any given_selection rules.\n" - "This message will not be repeated.\n"); - f_clause(c); - Already_warned = TRUE; - } - } } /* update_selectors */ +/*********************************************************************** Modif **************/ +/************* + * + * update_selectors2() + * + *************/ +/* + In case of ordering by rank we have to considere the case of bottom + + */ +static +void update_selectors2(Topform c, BOOL insert, int max_rank) +{ + BOOL matched = FALSE; + Plist p; + for (p = High.selectors; p; p = p->next) { + Giv_select gs = p->v; + if (eval_clause_in_rule(c, gs->property)) { + matched = TRUE; + if (insert) { + gs->idx = avl_insert(gs->idx, c, gs->compare); + High.occurrences++; + } + else { + + gs->idx = avl_delete(gs->idx, c, gs->compare); + High.occurrences--; + } + } + } + /* If it is high-priority, don't let it also be low priority. */ + if (!matched) { + for (p = Low.selectors; p; p = p->next) { + Giv_select gs = p->v; + if (eval_clause_in_rule(c, gs->property)) { + matched = TRUE; + if (insert) { + gs->idx = avl_insert(gs->idx, c, gs->compare); + Low.occurrences++; + } + else { + //Modif + //printf("yeah"); + //p_clause(c); + gs->idx = avl_delete(gs->idx, c, gs->compare); + Low.occurrences--; + } + } + } + } + if (!matched) { + static BOOL Already_warned = FALSE; + + if (!Already_warned) { + fprintf(stderr, "\n\nWARNING: one or more kept clauses do not match " + "any given_selection rules (see output).\n\n"); + printf("\nWARNING: the following clause does not match " + "any given_selection rules.\n" + "This message will not be repeated.\n"); + f_clause(c); + Already_warned = TRUE; + } + } +} /* update_selectors2 */ +/************* + * + * insert_into_sos3() + * + *************/ + +/* DOCUMENTATION + This routine appends a clause to the sos list and updates + the (private) index for extracting sos clauses. + */ + +/* PUBLIC */ +void insert_into_sos3(Topform c, Clist sos, int max_rank) +{ + if (Rule_needs_semantics) + set_semantics(c); /* in case not yet evaluated */ + + update_selectors2(c, TRUE,max_rank); + clist_append(c, sos); + Sos_size++; +} /* insert_into_sos2 */ +/*..............................................................................*/ /************* * * insert_into_sos2() @@ -324,6 +438,7 @@ Giv_select next_selector(Select_state s) /* PUBLIC */ BOOL givens_available(void) { + return (High.occurrences > 0 || Low.occurrences > 0); } /* givens_available */ @@ -338,28 +453,32 @@ BOOL givens_available(void) /* PUBLIC */ Topform get_given_clause2(Clist sos, int num_given, - Prover_options opt, char **type) + Prover_options opt, char **type) { - Topform giv; - Giv_select gs = next_selector(&High); - if (gs == NULL) - gs = next_selector(&Low); - if (gs == NULL) - return NULL; /* no clauses are available */ - - if (gs->order == GS_ORDER_RANDOM) { - int n = avl_size(gs->idx); - int i = (rand() % n) + 1; - giv = avl_nth_item(gs->idx, i); - } - else - giv = avl_smallest(gs->idx); - - *type = gs->name; - gs->selected += 1; - - remove_from_sos2(giv, sos); - return giv; + Topform giv; + Giv_select gs = next_selector(&High); + if (gs == NULL) + gs = next_selector(&Low); + if (gs == NULL) + return NULL; /* no clauses are available */ + //Modif + //if (gs->order == GS_ORDER_RANK) + // giv = avl_largest(gs->idx); + //********* End Modif ******* + else if (gs->order == GS_ORDER_RANDOM) { + int n = avl_size(gs->idx); + int i = (rand() % n) + 1; + giv = avl_nth_item(gs->idx, i); + // + } + else + giv = avl_smallest(gs->idx); + + *type = gs->name; + gs->selected += 1; + + remove_from_sos2(giv, sos); + return giv; } /* get_given_clause2 */ /************* @@ -657,43 +776,48 @@ Term selector_rule_term(char *name, char *priority, /* PUBLIC */ Plist selector_rules_from_options(Prover_options opt) { - Plist p = NULL; - - if (flag(opt->input_sos_first)) { - p = plist_append(p, selector_rule_term("I", "high", "age", - "initial", INT_MAX)); - } - - if (parm(opt->hints_part) == INT_MAX) { - p = plist_append(p, selector_rule_term("H", "high", "weight", - "hint", 1)); - } - else if (parm(opt->hints_part) > 0) { - p = plist_append(p, selector_rule_term("H", "low", "weight", - "hint", parm(opt->hints_part))); - } - - if (parm(opt->age_part) > 0) { - p = plist_append(p, selector_rule_term("A", "low", "age", - "all", parm(opt->age_part))); - } - if (parm(opt->false_part) > 0) { - p = plist_append(p, selector_rule_term("F", "low", "weight", - "false", parm(opt->false_part))); - } - if (parm(opt->true_part) > 0) { - p = plist_append(p, selector_rule_term("T", "low", "weight", - "true", parm(opt->true_part))); - } - if (parm(opt->weight_part) > 0) { - p = plist_append(p, selector_rule_term("W", "low", "weight", - "all", parm(opt->weight_part))); - } - if (parm(opt->random_part) > 0) { - p = plist_append(p, selector_rule_term("R", "low", "random", - "all", parm(opt->random_part))); - } - + Plist p = NULL; + + if (flag(opt->input_sos_first)) { + p = plist_append(p, selector_rule_term("I", "high", "age", + "initial", INT_MAX)); + } + + if (parm(opt->hints_part) == INT_MAX) { + p = plist_append(p, selector_rule_term("H", "high", "weight", + "hint", 1)); + } + else if (parm(opt->hints_part) > 0) { + p = plist_append(p, selector_rule_term("H", "low", "weight", + "hint", parm(opt->hints_part))); + } + + if (parm(opt->age_part) > 0) { + p = plist_append(p, selector_rule_term("A", "low", "age", + "all", parm(opt->age_part))); + } + if (parm(opt->false_part) > 0) { + p = plist_append(p, selector_rule_term("F", "low", "weight", + "false", parm(opt->false_part))); + } + if (parm(opt->true_part) > 0) { + p = plist_append(p, selector_rule_term("T", "low", "weight", + "true", parm(opt->true_part))); + } + if (parm(opt->weight_part) > 0) { + p = plist_append(p, selector_rule_term("W", "low", "weight", + "all", parm(opt->weight_part))); + } + if (parm(opt->random_part) > 0) { + p = plist_append(p, selector_rule_term("R", "low", "random", + "all", parm(opt->random_part))); + } + //*************** Modif + if (parm(opt->rank_part) > 0) { + p = plist_append(p, selector_rule_term("K", "low", "rank", + "all", parm(opt->rank_part))); + } + // *********** End Modif return p; } /* selector_rules_from_options */ diff --git a/provers.src/loop.c b/provers.src/loop.c new file mode 100644 index 0000000..cf641a1 --- /dev/null +++ b/provers.src/loop.c @@ -0,0 +1,436 @@ +/* + * loop.c + * + * + * Created by Abdelkader kersani on 22/05/12. + * Copyright 2012 LIG-CNRS. All rights reserved. + * + */ + +#include "loop.h" + +/* + return the empty clauses of a rank between I and J i.e J > rank > I + */ +Plist level_empty_clause(Plist g, int I, int J){ + if (isEmpty(g)) { + fatal_error("level_empty_clause : the list of empty clauses is empty"); + } + Plist p; + int rank ; + Plist res = NULL; + for (p = g; p; p = p->next){ + rank = get_rank(p->v) ; + if ( rank >= I && rank < J ) { + res=plist_prepend(res, p->v); + } + } + return res; + +} + +/* + return the empty clauses of a rank between I and J i.e J > rank >= I + */ +Plist level_empty_clause2(Plist g, int I, int J){ + if (isEmpty(g)) { + fatal_error("level_empty_clause : the list of empty clauses is empty"); + } + Plist p = g; + int rank ; + Ilist Tested_Rank = NULL; + int R=1; + Plist res = NULL; + int dif = J - I; + while (p && R <= dif){ + rank = get_rank(p->v) ; + //printf("ecl : ");p_clause(p->v); + if ( rank > I && rank <= J) { // les clauses vide ]i,i+j] + if(!ilist_member(Tested_Rank, rank)){ + res=plist_append(res, p->v); + //printf("res : ");p_plist(res); + Tested_Rank = ilist_append(Tested_Rank, rank); + //printf("TR : ");p_ilist(Tested_Rank); + R++; + //printf("R = %d",R); + } + } + p=p->next; + } + //printf("res1 : ");p_plist(res); + return res; + +} +/**/ +// returns true if the parents of Ci are in Si or they are of rank I and their parents are in Si +BOOL parents_in_Si(Plist Si, Topform Ci, int I){ + Topform c; + Ilist p; + BOOL res = TRUE; + Ilist parents = get_parents(Ci->justification, TRUE); + //printf("TT ");p_ilist(parents);printf(" TT "); p_clause(Ci); + for (p = parents; p; p = p->next) { + //printf("S %d ", p); + c = find_clause_by_id(p->i); + //printf("DDD"); + //p_clause(c); + if (!plist_member_clause(Si, c) && !bottom_clause(c) ) { + if(get_rank(c) < I){ + /*printf(" parents not in Si : ");p_clause(c); + p_plist(Si); + printf(" la clause en question ");p_clause(Ci);*/ + return FALSE; + } + else { + if (get_rank(c)==I) { + //printf("=="); + res = parents_in_Si(Si,c,I) ; + if (!res) { + return res; + } + } + //else { + // fatal_error("the rank of the parent is lower than the child"); + //} + + + } + } + + + + } + //printf("PPP"); + return res; +} +/* + Check whether Si generates Sij + + + + */ +BOOL generates(int I, Plist Si, Plist Sij){ + //p_plist(Si); + //p_plist(Sij); + if(isEmpty(Si)){ + return FALSE; + + } + if(isEmpty(Sij)) { + return TRUE; + } + Plist p, ancestor, tmp; + //Topform c; + for (p = Sij; p; p = p->next) {// for each clause of Sij + //p_clause(p->v); + //printf("I = %d", I); + //ancestor = hh(p->v, I); + + ancestor = get_clause_ancestors_ofrank(p->v, I); // we look for all its ancestors of rank I + //c=(Topform)p->v; + //ancestor = get_clanc_rank(c->id, NULL, I); + //printf("A");p_plist(ancestor); + if(isEmpty(ancestor)){// if there is no ancestors of rank I that means the class is not admissible + /*printf("the clause : "); + p_clause(p->v); + printf(" has as ancestors : "); + Plist ancetre = get_clause_ancestors(p->v); + p_plist(ancetre); + p_plist(ancestor);*/ + return FALSE; + //fatal_error("not admissible class"); + } + for (tmp = ancestor; tmp; tmp = tmp->next) {// for each ancestor + if(!plist_member_clause(Si, tmp->v) && !(bottom_clause(tmp->v)) ){ + /*printf(" \n Si : \n "); + //p_plist(Si); + printf("is a bottom clause = %d \n", bottom_clause(tmp->v)); + printf("the problem clause : ");p_clause(tmp->v); + printf("rank of the ancestor = %d \n" , get_rank(tmp->v));*/ + return FALSE; + } + + } + //free_plist(ancestor); + + } + //printf("C"); + return TRUE; +} + +/* + Check whether Si generates Sij + + + + */ +BOOL generates1(int I, Plist Si, Plist Sij){ + //p_plist(Si); + //p_plist(Sij); + int comp=0; + if(isEmpty(Si)){ + return FALSE; + + } + if(isEmpty(Sij)) { + return TRUE; + } + Plist p, ancestor, tmp; + //Topform c; + for (p = Sij; p; p = p->next) {// for each clause of Sij + //p_clause(p->v); + //printf("I = %d", I); + //ancestor = hh(p->v, I); + + ancestor = get_clause_ancestors_ofrank(p->v, I); // we look for all its ancestors of rank I + //c=(Topform)p->v; + //ancestor = get_clanc_rank(c->id, NULL, I); + //printf("A");p_clause(p->v); + //printf("X : %d ", comp); + //comp++; + if(isEmpty(ancestor)){// if there is no ancestors of rank I that means the class is not admissible + /*printf("the clause : "); + p_clause(p->v); + printf(" has as ancestors : "); + Plist ancetre = get_clause_ancestors(p->v); + p_plist(ancetre); + p_plist(ancestor); + //fatal_error("not admissible class2");*/ + return FALSE; + } + //printf("A");p_clause(p->v); + for (tmp = ancestor; tmp; tmp = tmp->next) {// for each ancestor + //printf("B"); + if(!plist_member_clause(Si, tmp->v)){ + //printf("C"); + //printf("CL is not in Si = %d", plist_member_clause(Si, tmp->v)); + + //p_clause(tmp->v); + //printf("D"); + if(!(bottom_clause(tmp->v))) { + + //printf("parents : %d ",parents_in_Si(Si,tmp->v,I) ); + if (!parents_in_Si(Si,tmp->v,I)) { + /*printf(" \n Si : \n "); + //p_plist(Si); + printf("is a bottom clause = %d \n", bottom_clause(tmp->v)); + printf("the problem clause : ");p_clause(tmp->v); + printf("rank of the ancestor = %d \n" , get_rank(tmp->v));*/ + return FALSE; + } + //printf("A"); + } + } + + } + //free_plist(ancestor); + + } + //printf("C"); + return TRUE; +} + +/* + + retourne une clause C de Si telle que shift(C) n'est pas subsumée par aucune clause de Sij. + + */ +Topform find_notsubsumedcl(Plist Si, Plist Sij, int J){ + Plist p, anc, tmp; + BOOL state=TRUE; + for (p = Si; p; p = p->next) {/*for each clause of Si */ + state = TRUE; + + Topform cij = shift_cl(p->v, J);/*compute its shift clause*/ + //printf("r1\n"); printf(" J = %d ", J) ;p_clause(cij); printf("r1\n"); + int n=0; + for (tmp = Sij; tmp; tmp = tmp->next) { /*for each clause de Sij*/ + //printf("n = %d ", n);p_clause(tmp->v); + if(state){ + // + Topform top=tmp->v; + //printf("r0\n");p_clause(cij); printf("r0\n"); + //printf("r1\n");p_clause(top); printf("r1\n"); + + if(subsumes_param(tmp->v, cij)){//if its shift occurs in Sij then it's subsumed + //printf("kk"); + state = FALSE; + //return NULL; + } + } + + } + if (state) { + return p->v; + } + } + return NULL; +} +/* + + retourne une clause C de Si telle que shift(C) n'est pas égal à aucune clause de Sij. + + */ +Topform find_notequalcl(Plist Si, Plist Sij, int J){ + Plist p, anc, tmp; + BOOL state=TRUE; + for (p = Si; p; p = p->next) {/*for each clause of Si */ + state = TRUE; + + Topform cij = shift_cl(p->v, J);/*compute its shift clause*/ + /*printf("r1\n");p_clause(cij); printf("r1\n"); + printf("K\n");p_clause(cij);printf("K\n");*/ + int n=0; + for (tmp = Sij; tmp; tmp = tmp->next) { /*for each clause de Sij*/ + //printf("n = %d ", n);p_clause(tmp->v); + if(state){ + //if(subsumes_param(tmp->v, cij)){ + Topform top=tmp->v; + //printf("r0\n");p_clause(cij); printf("r0\n"); + //printf("r1\n");p_clause(top); printf("r1\n"); + + if(clause_ident_order(top,cij)){//if its shift occurs in Sij then it's subsumed + //printf("kk"); + state = FALSE; + //return NULL; + } + } + + } + if (state) { + return p->v; + } + } + return NULL; +} +/* + + + + + + + +BOOL parent_emptycl(Topform Ci){ + Plist anc=get_clause_ancestors_ofrank(C, I); + +}*/ + +/* + retourne toutes les clause de g de rang I + */ +Plist look_by_rank(Plist g, int I){ + Plist p, res; + res=NULL; + for (p = g; p; p = p->next) { + if((get_rank(p->v) == I) && get_var_term(p->v)) + res=plist_prepend(res, p->v); + } + return res; +} +/* + Return all the clauses of g of rank I + the clauses are Si-flat if index_flat is true + */ +Plist look_by_rank2(Plist g, int I, BOOL index_flat){ + Plist p, res; + res=NULL; + for (p = g; p; p = p->next) { + if((get_rank(p->v) == I) && get_var_term(p->v)){ + if (index_flat) { + if (iflat(I,p->v)) { + res=plist_prepend(res, p->v); + } + } + else { + res=plist_prepend(res, p->v); + } + + + + } + } + return res; +} +BOOL is_ancestor(int I,Topform Ci, Topform Cij){ + Plist ancestors = get_clause_ancestors_ofrank(Cij, I); + return plist_member_clause(ancestors, Ci); +} +/* + retourne toutes les clauses + */ +Plist get_empty_clauses(Plist g, int I, int IJ){ + Plist p, res; + res=NULL; + int rank; + for (p = g; p; p = p->next) { + rank =get_rank(p->v); + if(rank < IJ && rank >= I ) + if (pureparam_cst_topform(p->v)) { + + res=plist_prepend(res, p->v); + } + /*else { + fatal_error("get_empty_clauses : it's not an empty clause"); + }*/ + + + } + //printf("res : "); + //p_plist(res); + return res; +} +/* PUBLIC */ +/* Return u if a Plist lst contains a topform u and else return NULL*/ +Topform plist_member_clause_shift(Plist lst, void *u) +{ + if (lst == NULL) + return NULL; + else{ + Topform v1 =lst->v; + Topform v2 = (Topform)u; + /*if(get_rank(v1) == 1){ + printf("Begin"); + p_clause(v2); + p_clause(v1); + }*/ + if (clause_ident_order(v1, v2)){ + //printf(" egal "); + + return v1; + } + else{ + //printf(" pasegal "); + + return plist_member_clause_shift(lst->next, v2); + } + } +} /* plist_member_clause */ + +/* + Check whether + + + + + */ + +int compute_rank_max(BOOL* tab){ + int res = 0; + while (res <= 40 && tab[res]) { + res++; + + } + return res - 1; + +} +void init_tab_rank(BOOL* tab){ + int res = 1; + while (res <= 40 ) { + tab[res]=FALSE; + res++; + + } +} + + diff --git a/provers.src/loop.h b/provers.src/loop.h new file mode 100644 index 0000000..5c3ae6a --- /dev/null +++ b/provers.src/loop.h @@ -0,0 +1,49 @@ +/* + * loop.h + * + * + * Created by Abdelkader kersani on 22/05/12. + * Copyright 2012 LIG-CNRS. All rights reserved. + * + */ +#ifndef TP_LOOP_H + +#include "search-structures.h" + + + +#include "../ladr/literals.h" +#include "../ladr/attrib.h" +#include "../ladr/formula.h" +#include "../ladr/maximal.h" + +BOOL generates(int I, Plist Si, Plist Sij); + + + +Topform find_notsubsumedcl(Plist Si, Plist Sij, int J); + +Topform find_notequalcl(Plist Si, Plist Sij, int J); + +Plist look_by_rank(Plist g, int I); + +Plist look_by_rank2(Plist g, int I, BOOL index_flat); + +Plist get_empty_clauses(Plist g, int I, int IJ); + +//BOOL fixed_point(int I, int J, Plist Si, Plist Sij, Plist EmptyCl); + +//BOOL fixed_point_alg(int I, int J, Clist sos, Clist usable, Plist EmptyCl); + +//BOOL fixed_point_without_empties(int I, int J, Clist sos, Clist usable); + +Plist level_empty_clause(Plist g, int I, int J); + +Plist level_empty_clause2(Plist g, int I, int J); + +Topform plist_member_clause_shift(Plist lst, void *u); + +int compute_rank_max(BOOL* tab); +void init_tab_rank(BOOL* tab); + +#endif \ No newline at end of file diff --git a/provers.src/pred_elim.c b/provers.src/pred_elim.c index 8b9352d..786d844 100644 --- a/provers.src/pred_elim.c +++ b/provers.src/pred_elim.c @@ -89,18 +89,19 @@ BOOL eliminable_relation(int symbol, Plist clauses, BOOL equality) static Ilist eliminable_relations(Plist clauses, BOOL equality) { - Ilist rsyms = rsym_set_in_topforms(clauses); - Ilist eliminable = NULL; - Ilist p; - for (p = rsyms; p; p = p->next) { - if (!is_eq_symbol(p->i) && /* don't allow equalities */ - sn_to_arity(p->i) != 0 && /* don't allow prop atoms */ - eliminable_relation(p->i, clauses, equality)) - - eliminable = ilist_append(eliminable, p->i); - } - zap_ilist(rsyms); - return eliminable; + Ilist rsyms = rsym_set_in_topforms(clauses); + Ilist eliminable = NULL; + Ilist p; + for (p = rsyms; p; p = p->next) { + if (!is_eq_symbol(p->i) && /* don't allow equalities */ + sn_to_arity(p->i) != 0 && + !is_param_symbol(p->i) && /* don't allow prop atoms */ + eliminable_relation(p->i, clauses, equality)) + + eliminable = ilist_append(eliminable, p->i); + } + zap_ilist(rsyms); + return eliminable; } /* eliminable_relations */ /************* @@ -207,32 +208,34 @@ Plist incorporate_new_clauses(Plist sos, Plist new, BOOL echo) static Plist elim_relation(int symbol, Plist sos, Clist disabled, BOOL echo) { - /* this does a naive given-clause loop */ - Plist usable = NULL; - while (sos) { - Plist new; - Topform given = sos->v; - sos = plist_pop(sos); - usable = plist_append(usable, given); + /* this does a naive given-clause loop */ + Plist usable = NULL; + while (sos) { + Plist new; + Topform given = sos->v; + sos = plist_pop(sos); + usable = plist_append(usable, given); #ifdef GEN_DEBUG - printf("\ngiven: "); f_clause(given); + printf("\ngiven: "); f_clause(given); #endif - new = gen_given(symbol, given, usable); - sos = incorporate_new_clauses(sos, new, echo); - } - /* partition usable into clauses with and without symbol */ - { - Plist without = NULL; - Plist p; - for (p = usable; p; p = p->next) { - if (rsym_occurrences(symbol, p->v) > 0) - clist_append(p->v, disabled); - else - without = plist_append(without, p->v); - } - zap_plist(usable); - return without; - } + new = gen_given(symbol, given, usable); + sos = incorporate_new_clauses(sos, new, echo); + } + /* partition usable into clauses with and without symbol */ + { + Plist without = NULL; + Plist p; + for (p = usable; p; p = p->next) { + if (rsym_occurrences(symbol, p->v) > 0) + clist_append(p->v, disabled); + else + without = plist_append(without, p->v); + + + } + zap_plist(usable); + return without; + } } /* elim_relation */ /************* @@ -255,30 +258,31 @@ the end result do not have IDs. /* PUBLIC */ void predicate_elimination(Clist clauses, Clist disabled, BOOL echo) { - Plist clauses2 = prepend_clist_to_plist(NULL, clauses); - BOOL equality = equality_in_clauses(clauses2); /* eq => different method */ - Ilist syms = eliminable_relations(clauses2, equality); - - if (syms == NULL) { - zap_plist(clauses2); - if (echo) - printf("\nNo predicates eliminated.\n"); - } - else { - clist_remove_all_clauses(clauses); - while (syms) { - /* use first symbol, discard rest, get new list */ - if (echo) - printf("\nEliminating %s/%d\n", - sn_to_str(syms->i), - sn_to_arity(syms->i)); + Plist clauses2 = prepend_clist_to_plist(NULL, clauses); + BOOL equality = equality_in_clauses(clauses2); /* eq => different method */ - clauses2 = elim_relation(syms->i, clauses2, disabled, echo); - zap_ilist(syms); - syms = eliminable_relations(clauses2, equality); - } - clist_append_plist(clauses, clauses2); - zap_plist(clauses2); - } + Ilist syms = eliminable_relations(clauses2, equality); + + if (syms == NULL) { + zap_plist(clauses2); + if (echo) + printf("\nNo predicates eliminated.\n"); + } + else { + clist_remove_all_clauses(clauses); + while (syms) { + /* use first symbol, discard rest, get new list */ + if (echo) + printf("\nEliminating %s/%d\n", + sn_to_str(syms->i), + sn_to_arity(syms->i)); + + clauses2 = elim_relation(syms->i, clauses2, disabled, echo); + zap_ilist(syms); + syms = eliminable_relations(clauses2, equality); + } + clist_append_plist(clauses, clauses2); + zap_plist(clauses2); + } } /* predicate_elimination */ diff --git a/provers.src/search-structures.h b/provers.src/search-structures.h index 4ce8c30..2dc3fb5 100644 --- a/provers.src/search-structures.h +++ b/provers.src/search-structures.h @@ -20,6 +20,7 @@ #define TP_SEARCH_STRUCTURES_H #include "../ladr/ladr.h" +//#include "../ladr/loop.h" // Attributes @@ -105,6 +106,7 @@ struct prover_options { lightest_first, default_parts, random_given, + rank_given, //Modif breadth_first_hints, automatic, // auto is a reserved symbol in C! @@ -116,7 +118,13 @@ struct prover_options { auto2, // enhanced auto mode raw, production, - + + superind, // Modif launch superind + sat, // Detect satisfiability + cycle1, //Modif : launch cycle1 flag + cycle2, //Modif : launch cycle2 flag + index_flat, // Modif : use only index_flat clauses + random_loopdet, //Modif : use a random loop detection lex_order_vars, // others ignore_option_dependencies; @@ -145,6 +153,8 @@ struct prover_options { true_part, false_part, random_part, + rank_part, //Modif + start_rank, //Modif random_seed, eval_limit, eval_var_limit, diff --git a/provers.src/search.c b/provers.src/search.c index b89e923..435edb3 100644 --- a/provers.src/search.c +++ b/provers.src/search.c @@ -1,4 +1,4 @@ -/* Copyright (C) 2006, 2007 William McCune + /* Copyright (C) 2006, 2007 William McCune This file is part of the LADR Deduction Library. @@ -62,7 +62,21 @@ static struct { Clist limbo; Clist disabled; Plist empties; - + /*******************MODIF*/ + Plist rank_emptycl; + Topform loop_clause;// a clause of the for N^j(X) + BOOL loop; + int incr; + int max_rank;// the greatest rank of a generated clause + Plist SI; + Plist SIJ; + BOOL tab_rank [40]; + Plist empty_clauses; + BOOL ind_empty_clause; + int current_rank;//the current rank + int number_of_calls; + BOOL admissible;// True if the class is admissible +/*************************/ // indexing Lindex clashable_idx; // literal index for resolution rules @@ -167,6 +181,9 @@ Prover_options init_prover_options(void) p->breadth_first = init_flag("breadth_first", FALSE); p->lightest_first = init_flag("lightest_first", FALSE); p->random_given = init_flag("random_given", FALSE); + /*************************************Modif*********/ + p->rank_given = init_flag("rank_given", FALSE); + /*.........................................*/ p->breadth_first_hints = init_flag("breadth_first_hints", FALSE); p->default_parts = init_flag("default_parts", TRUE); @@ -181,7 +198,14 @@ Prover_options init_prover_options(void) p->production = init_flag("production", FALSE); p->lex_order_vars = init_flag("lex_order_vars", FALSE); - + /**********************************Modif*****Add the loop detection flag**********/ + p->superind = init_flag("superind", TRUE); // launch the loop detection + p->sat = init_flag("sat", TRUE); // launch the loop detection + p->cycle1 = init_flag("cycle1", TRUE); // loop detection algorithme based on the search of smallest fixed point + p->cycle2 = init_flag("cycle2", FALSE);// loop detection algorithme based on the search of largest fixed point + p->index_flat = init_flag("index_flat", FALSE);// apply the loop detection on sets of index_flat clauses + p->random_loopdet = init_flag("random_loopdet", FALSE); // launch the loop detection + /*.................................................*/ // PARMS: // internal name external name default min max @@ -207,6 +231,10 @@ Prover_options init_prover_options(void) p->false_part = init_parm("false_part", 4, 0,INT_MAX); p->true_part = init_parm("true_part", 4, 0,INT_MAX); p->random_part = init_parm("random_part", 0, 0,INT_MAX); + //Modif + p->rank_part = init_parm("rank_part", 0, 0,INT_MAX); + p->start_rank = init_parm("start_rank", 2, 0,INT_MAX); + //********* End Modif p->random_seed = init_parm("random_seed", 0, -1,INT_MAX); p->eval_limit = init_parm("eval_limit", 1024, -1,INT_MAX); p->eval_var_limit = init_parm("eval_var_limit", -1, -1,INT_MAX); @@ -286,6 +314,12 @@ Prover_options init_prover_options(void) flag_parm_dependency(p->para_units_only, TRUE, p->para_lit_limit, 1); flag_parm_dep_default(p->para_units_only, FALSE, p->para_lit_limit); +/********** Modif *********/ + flag_flag_dependency(p->superind, FALSE, p->cycle1, FALSE); + flag_flag_dependency(p->superind, FALSE, p->cycle2, FALSE); + flag_flag_dependency(p->cycle1, TRUE, p->cycle2, FALSE); + flag_flag_dependency(p->cycle2, TRUE, p->cycle1, FALSE); +/*************************/ flag_flag_dependency(p->hyper_resolution, TRUE, p->pos_hyper_resolution, TRUE); flag_flag_dependency(p->hyper_resolution, FALSE, p->pos_hyper_resolution, FALSE); @@ -304,6 +338,9 @@ Prover_options init_prover_options(void) parm_parm_dependency(p->pick_given_ratio, p->false_part, 0, FALSE); parm_parm_dependency(p->pick_given_ratio, p->true_part, 0, FALSE); parm_parm_dependency(p->pick_given_ratio, p->random_part, 0, FALSE); + //************ Modif + parm_parm_dependency(p->pick_given_ratio, p->rank_part, 0, FALSE); + //********** End Modif flag_parm_dependency(p->lightest_first, TRUE, p->weight_part, 1); flag_parm_dependency(p->lightest_first, TRUE, p->age_part, 0); @@ -311,6 +348,9 @@ Prover_options init_prover_options(void) flag_parm_dependency(p->lightest_first, TRUE, p->true_part, 0); flag_parm_dependency(p->lightest_first, TRUE, p->random_part, 0); flag_flag_dependency(p->lightest_first, FALSE, p->default_parts, TRUE); + //************ Modif + flag_parm_dependency(p->lightest_first, TRUE, p->rank_part, 0); + //********** End Modif flag_parm_dependency(p->random_given, TRUE, p->weight_part, 0); flag_parm_dependency(p->random_given, TRUE, p->age_part, 0); @@ -318,13 +358,35 @@ Prover_options init_prover_options(void) flag_parm_dependency(p->random_given, TRUE, p->true_part, 0); flag_parm_dependency(p->random_given, TRUE, p->random_part, 1); flag_flag_dependency(p->random_given, FALSE, p->default_parts, TRUE); - + + //************ Modif + flag_parm_dependency(p->random_given, TRUE, p->rank_part, 0); + //********** End Modif + +//********************************** Modif ******************************* + + flag_parm_dependency(p->rank_given, TRUE, p->weight_part, 0); + flag_parm_dependency(p->rank_given, TRUE, p->age_part, 0); + flag_parm_dependency(p->rank_given, TRUE, p->false_part, 0); + flag_parm_dependency(p->rank_given, TRUE, p->true_part, 0); + flag_parm_dependency(p->rank_given, TRUE, p->random_part, 0); + flag_flag_dependency(p->rank_given, FALSE, p->default_parts, TRUE); + + //************ Modif + flag_parm_dependency(p->rank_given, TRUE, p->rank_part, 1); + //********** End Modif + +//********************************** End Modif ***************************** flag_parm_dependency(p->breadth_first, TRUE, p->age_part, 1); flag_parm_dependency(p->breadth_first, TRUE, p->weight_part, 0); flag_parm_dependency(p->breadth_first, TRUE, p->false_part, 0); flag_parm_dependency(p->breadth_first, TRUE, p->true_part, 0); flag_parm_dependency(p->breadth_first, TRUE, p->random_part, 0); flag_flag_dependency(p->breadth_first, FALSE, p->default_parts, TRUE); + + //************ Modif + flag_parm_dependency(p->breadth_first, TRUE, p->rank_part, 0); + //********** End Modif /* flag_parm_dependency(p->default_parts, TRUE, p->hints_part, INT_MAX); */ flag_parm_dependency(p->default_parts, TRUE, p->age_part, 1); @@ -332,6 +394,10 @@ Prover_options init_prover_options(void) flag_parm_dependency(p->default_parts, TRUE, p->false_part, 4); flag_parm_dependency(p->default_parts, TRUE, p->true_part, 4); flag_parm_dependency(p->default_parts, TRUE, p->random_part, 0); + + //************ Modif + flag_parm_dependency(p->default_parts, TRUE, p->rank_part, 0); + //********** End Modif /* flag_parm_dependency(p->default_parts, FALSE, p->hints_part, 0); */ flag_parm_dependency(p->default_parts, FALSE, p->age_part, 0); @@ -339,7 +405,10 @@ Prover_options init_prover_options(void) flag_parm_dependency(p->default_parts, FALSE, p->false_part, 0); flag_parm_dependency(p->default_parts, FALSE, p->true_part, 0); flag_parm_dependency(p->default_parts, FALSE, p->random_part, 0); - + + //************ Modif + flag_parm_dependency(p->default_parts, FALSE, p->rank_part, 0); + //********** End Modif /***********************/ flag_flag_dependency(p->default_output, TRUE, p->quiet, FALSE); @@ -570,7 +639,7 @@ void fprint_prover_stats(FILE *fp, struct prover_stats s, char *stats_level) fprintf(fp,"Megabytes=%.2f.\n", s.kbyte_usage / 1000.0); #if 1 - fprintf(fp,"User_CPU=%.2f, System_CPU=%.2f, Wall_clock=%u.\n", + fprintf(fp,"User_CPU=%.3f, System_CPU=%.2f, Wall_clock=%u.\n", user_seconds(), system_seconds(), wallclock()); #else /* some debugging junk */ { @@ -996,6 +1065,7 @@ void free_search_memory(void) static void handle_proof_and_maybe_exit(Topform empty_clause) { + Term answers; Plist proof, p; @@ -1074,6 +1144,159 @@ void handle_proof_and_maybe_exit(Topform empty_clause) zap_plist(proof); } // handle_proof_and_maybe_exit +/******************************************************Modif**************************/ + +/************* + * + * handle_proof() + * + *************/ + +static +void handle_proof(Topform empty_clause) +{ + + Term answers; + Plist proof, p; + + mark_parents_as_used(empty_clause); + //assign_clause_id(empty_clause); + proof = get_clause_ancestors(empty_clause); + uncompress_clauses(proof); + + if (!flag(Opt->reuse_denials) && Glob.horn) { + Topform c = first_negative_clause(proof); + if (clause_member_plist(Glob.desc_to_be_disabled, c)) { + printf("%% Redundant proof: "); + f_clause(empty_clause); + return; + } + else + /* Descendants of c will be disabled when it is safe to do so. */ + Glob.desc_to_be_disabled = plist_prepend(Glob.desc_to_be_disabled, c); + } + + Glob.empties = plist_append(Glob.empties, empty_clause); + Stats.proofs++; + + answers = get_term_attributes(empty_clause->attributes, Att.answer); + + /* message to stderr */ + + if (!flag(Opt->quiet)) { + fflush(stdout); + if (flag(Opt->bell)) + bell(stderr); + //fprintf(stderr, "-------- Proof %d -------- ", Stats.proofs); + if (answers != NULL) + fwrite_term_nl(stderr, answers); + else + fprintf(stderr, "\n"); + } + + /* print proof to stdout */ + + fflush(stderr); + if (flag(Opt->print_proofs)) { + print_separator(stdout, "PROOF of level empty clauses", TRUE); + //printf("\n%% Proof %d at %.2f (+ %.2f) seconds", + // Stats.proofs, user_seconds(), system_seconds()); + if (answers != NULL) { + // printf(": "); + fwrite_term(stdout, answers); + } + printf(".\n"); + + printf("%% Length of proof is %d.\n", proof_length(proof)); + //printf("%% Level of proof is %d.\n", clause_level(empty_clause)); + //printf("%% Maximum clause weight is %.3f.\n", max_clause_weight(proof)); + //printf("%% Given clauses %d.\n\n", Stats.given); + for (p = proof; p; p = p->next) + fwrite_clause(stdout, p->v, CL_FORM_STD); + print_separator(stdout, "end of proof", TRUE); + } /* print_proofs */ + else { + //printf("\n-------- Proof %d at (%.2f + %.2f seconds) ", + // Stats.proofs, user_seconds(), system_seconds()); + if (answers != NULL) + fwrite_term_nl(stdout, answers); + else + fprintf(stdout, "\n"); + } + fflush(stdout); + if (answers) + zap_term(answers); + + //actions_in_proof(proof, &Att); /* this can exit */ + + //if (at_parm_limit(Stats.proofs, Opt->max_proofs)) + // done_with_search(MAX_PROOFS_EXIT); /* does not return */ + + zap_plist(proof); +} // handle_proof_and_maybe_exit +/************* + * + * handle_proof_and_maybe_exit2() + * + *************/ + +static +void handle_proof_and_maybe_exit2() +{ + Plist proof, p; + + + proof = NULL; + Stats.proofs=1; + + + /* print proof to stdout */ + + fflush(stderr); + if (isEmpty(Glob.SI)) { + print_separator(stdout, "PROOF", TRUE); + printf("\n%% Proof %d at %.3f (+ %.3f) seconds", + Stats.proofs, user_seconds(), system_seconds()); + printf(".\n"); + + //printf("%% Length of proof is %d.\n", proof_length(proof)); + printf("%% Given clauses %d.\n\n", Stats.given); + printf("%% Cet ensemble est satisfaisable \n"); + printf("%% un modèle possible : n = %d", Glob.max_rank + 1); + } else{ + if (flag(Opt->print_proofs)) { + print_separator(stdout, "PROOF", TRUE); + printf("\n%% Proof %d at %.3f (+ %.3f) seconds", + Stats.proofs, user_seconds(), system_seconds()); + printf(".\n"); + + //printf("%% Length of proof is %d.\n", proof_length(proof)); + printf("%% Given clauses %d.\n\n", Stats.given); + printf("%% number of calls to fixpoint : %d \n", Glob.number_of_calls); + + for (p = proof; p; p = p->next) + fwrite_clause(stdout, p->v, CL_FORM_STD); + printf(" S_init : \n "); + p_plist_param(Glob.SI); + printf("\n"); + printf(" S_loop : \n "); + p_plist_param(Glob.SIJ); + printf("\n"); + printf(" The empty clauses : \n "); + //p_plist_param(get_empty_clauses(Glob.rank_emptycl, 0,get_rank(Glob.SIJ->v) )); + p_plist_param(level_empty_clause2(Glob.rank_emptycl, -1, get_rank(Glob.SIJ->v))); + printf("max_rank %d \n",Glob.max_rank); + print_separator(stdout, "end of proof", TRUE); + //handle_proof(Glob.rank_emptycl->v); + } /* print_proofs */ + } + fflush(stdout); + + done_with_search(MAX_PROOFS_EXIT); /* does not return */ + + zap_plist(proof); +} // handle_proof_and_maybe_exit2 + /************* * @@ -1187,14 +1410,18 @@ void cl_process_simplify(Topform c) static void cl_process_keep(Topform c) { - Stats.kept++; + Stats.kept++; if (!c->normal_vars) renumber_variables(c, MAX_VARS); + + if (c->id == 0) assign_clause_id(c); // unit conflict or input: already has ID mark_parents_as_used(c); + //printf("c = "); p_clause(c); mark_maximal_literals(c->literals); mark_selected_literals(c->literals, stringparm1(Opt->literal_selection)); + if (c->matching_hint != NULL) keep_hint_matcher(c); @@ -1260,6 +1487,7 @@ void cl_process_new_demod(Topform c) static BOOL skip_black_white_tests(Topform c) { + //return TRUE; return (!Glob.searching || c->used || restricted_denial(c) || @@ -1269,64 +1497,110 @@ BOOL skip_black_white_tests(Topform c) static BOOL cl_process_delete(Topform c) { - // Should the clause be deleted (tautology, limits, subsumption)? - - if (true_clause(c->literals)) { // tautology - if (flag(Opt->print_gen)) - printf("tautology\n"); - Stats.subsumed++; - return TRUE; // delete - } - - clause_wt_with_adjustments(c); // possibly sets c->matching_hint - - // White-black tests - - if (!skip_black_white_tests(c)) { - if (white_tests(c)) { - if (flag(Opt->print_gen)) - printf("keep_rule applied.\n"); - Stats.kept_by_rule++; - } - else { - if (black_tests(c)) { - if (flag(Opt->print_gen)) - printf("delete_rule applied.\n"); - Stats.deleted_by_rule++; - return TRUE; //delete - } - else if (!sos_keep2(c, Glob.sos, Opt)) { - if (flag(Opt->print_gen)) - printf("sos_limit applied.\n"); - Stats.sos_limit_deleted++; - return TRUE; // delete - } - } - } - - // Forward subsumption - - { - Topform subsumer; - clock_start(Clocks.subsume); - subsumer = forward_subsumption(c); - clock_stop(Clocks.subsume); - if (subsumer != NULL && !c->used) { - if (flag(Opt->print_gen)) - printf("subsumed by %d.\n", subsumer->id); - Stats.subsumed++; - return TRUE; // delete - } - else - return FALSE; // keep the clause - } + // Should the clause be deleted (tautology, limits, subsumption, normalized)? + + if (true_clause(c->literals)) { // tautology + if (flag(Opt->print_gen)) + printf("tautology\n"); + Stats.subsumed++; + return TRUE; // delete + } + + /**********MIDIF**********/ + if (flag(Opt->superind)) { + + if(!(is_normalized(c)) || !alpha_C_clause(c)){ + if(flag(Opt->print_gen)){ + printf("not normalized \n"); + + } + return TRUE; + } + if(get_rank(c)== -2){ + if(flag(Opt->print_gen)){ + printf("the m.g.u is at least of the form s(s(x)) \n"); + Glob.admissible = FALSE; + p_clause(c); + printf(""); + } + return TRUE; + } + if(get_rank(c)== -3){ + if(flag(Opt->print_gen)){ + printf("it's not an (alpha-C)- clause \n"); + Glob.admissible = FALSE; + //printf("alpha C %d \n",alpha_C_clause(c)); + printf(""); + //p_clause(c); + } + + return TRUE; + } + } + /**********************/ + clause_wt_with_adjustments(c); // possibly sets c->matching_hint + + // White-black tests + + if (!skip_black_white_tests(c)) { //Modif temporaire black and white test ?? + if (white_tests(c)) { + if (flag(Opt->print_gen)) + printf("keep_rule applied.\n"); + Stats.kept_by_rule++; + } + else { + if (black_tests(c)) { + if (flag(Opt->print_gen)) + printf("delete_rule applied.\n"); + Stats.deleted_by_rule++; + return TRUE; //delete + } + else if (!sos_keep2(c, Glob.sos, Opt)) { + if (flag(Opt->print_gen)) + printf("sos_limit applied.\n"); + Stats.sos_limit_deleted++; + return TRUE; // delete + } + } + } + + // Forward subsumption + + { + Topform subsumer ; + clock_start(Clocks.subsume); + subsumer = forward_subsumption(c); + clock_stop(Clocks.subsume); + if (subsumer != NULL && !c->used) { + //printf("I I "); + //p_clause(c); + //p_clause(subsumer); + //printf("J J\n"); + if((param_free(c) && !param_free(subsumer)) || (!param_free(c) && param_free(subsumer)) ){ + printf("La clause "); + p_clause(c); + printf(" est subsumée par "); + p_clause(subsumer); + printf(" Fin \n"); + } + if (flag(Opt->print_gen)) + printf("subsumed by %d.\n", subsumer->id); + Stats.subsumed++; + return TRUE; // delete + //} + //else + //return FALSE; + } + else + return FALSE; // keep the clause + } } // cl_process_delete static void cl_process(Topform c) { // If the infer_clock is running, stop it and restart it when done. - + BOOL infer_clock_stopped = FALSE; if (clock_running(Clocks.infer)) { clock_stop(Clocks.infer); @@ -1344,33 +1618,45 @@ void cl_process(Topform c) printf("\ngenerated: "); fwrite_clause(stdout, c, CL_FORM_STD); } - + cl_process_simplify(c); // all simplification - - if (number_of_literals(c->literals) == 0) // empty clause + +/*************************MODIF*****************************/ + + /*********************************************************/ + if (number_of_literals(c->literals) == 0 || loop_clause(c) ) // empty clause handle_proof_and_maybe_exit(c); - else { - // Do safe unit conflict before any deletion checks. - if (flag(Opt->safe_unit_conflict)) - cl_process_conflict(c, FALSE); // marked as used if conflict - - if (cl_process_delete(c)) - delete_clause(c); - else { - cl_process_keep(c); - // Ordinary unit conflict. - if (!flag(Opt->safe_unit_conflict)) - cl_process_conflict(c, FALSE); - cl_process_new_demod(c); - // We insert c into the literal index now so that it will be - // available for unit conflict and forward subsumption while - // it's in limbo. (It should not be back subsumed while in limbo. - // See fatal error in limbo_process). - index_literals(c, INSERT, Clocks.index, FALSE); - clist_append(c, Glob.limbo); - } // not deleted - } // not empty clause - + else {//*********************Modif ************* + if(loop_clause(c)){ + Glob.loop_clause = c; + Glob.loop =TRUE; + }else{//*********************************** + // Do safe unit conflict before any deletion checks. + if (flag(Opt->safe_unit_conflict)) + cl_process_conflict(c, FALSE); // marked as used if conflict + + if (cl_process_delete(c)) + delete_clause(c); + else { + cl_process_keep(c); + // Ordinary unit conflict. + if (!flag(Opt->safe_unit_conflict)) + cl_process_conflict(c, FALSE); + cl_process_new_demod(c); + // We insert c into the literal index now so that it will be + // available for unit conflict and forward subsumption while + // it's in limbo. (It should not be back subsumed while in limbo. + // See fatal error in limbo_process). + index_literals(c, INSERT, Clocks.index, FALSE); + init_rank(c); + clist_append(c, Glob.limbo); + } // not deleted + }// not a loop_clause + }// not empty clause + // Modif + + + /*.............................................*/ clock_stop(Clocks.preprocess); if (infer_clock_stopped) clock_start(Clocks.infer); @@ -1434,32 +1720,32 @@ void back_demod(Topform demod) static void back_unit_deletion(Topform unit) { - Plist results, p, prev; - - clock_start(Clocks.back_unit_del); - results = back_unit_deletable(unit); - clock_stop(Clocks.back_unit_del); - p = results; - while(p != NULL) { - Topform old = p->v; - if (!clist_member(old, Glob.disabled)) { - Topform new; - if (flag(Opt->basic_paramodulation)) - new = copy_clause_with_flag(old, nonbasic_flag()); - else - new = copy_clause(old); - Stats.back_unit_deleted++; - if (flag(Opt->print_kept)) - printf(" %d back unit deleting %d.\n", unit->id, old->id); - new->justification = back_unit_deletion_just(old); - new->attributes = inheritable_att_instances(old->attributes, NULL); - disable_clause(old); - cl_process(new); - } - prev = p; - p = p->next; - free_plist(prev); - } + Plist results, p, prev; + + clock_start(Clocks.back_unit_del); + results = back_unit_deletable(unit); + clock_stop(Clocks.back_unit_del); + p = results; + while(p != NULL) { + Topform old = p->v; + if (!clist_member(old, Glob.disabled)) { + Topform new; + if (flag(Opt->basic_paramodulation)) + new = copy_clause_with_flag(old, nonbasic_flag()); + else + new = copy_clause(old); + Stats.back_unit_deleted++; + if (flag(Opt->print_kept)) + printf(" %d back unit deleting %d.\n", unit->id, old->id); + new->justification = back_unit_deletion_just(old); + new->attributes = inheritable_att_instances(old->attributes, NULL); + disable_clause(old); + cl_process(new); + } + prev = p; + p = p->next; + free_plist(prev); + } } // back_unit_deletion /************* @@ -1475,26 +1761,26 @@ void back_unit_deletion(Topform unit) static void back_cac_simplify(void) { - Plist to_delete = NULL; - Plist a; - Clist_pos p; - for (p = Glob.sos->first; p; p = p->next) { - if (cac_tautology(p->c->literals)) - to_delete = plist_prepend(to_delete, p->c); - } - for (p = Glob.usable->first; p; p = p->next) { - if (cac_tautology(p->c->literals)) - to_delete = plist_prepend(to_delete, p->c); - } - for (p = Glob.limbo->first; p; p = p->next) { - if (cac_tautology(p->c->literals)) - to_delete = plist_prepend(to_delete, p->c); - } - for (a = to_delete; a; a = a->next) { - printf("%% back CAC tautology: "); f_clause(a->v); - disable_clause(a->v); - } - zap_plist(to_delete); /* shallow */ + Plist to_delete = NULL; + Plist a; + Clist_pos p; + for (p = Glob.sos->first; p; p = p->next) { + if (cac_tautology(p->c->literals)) + to_delete = plist_prepend(to_delete, p->c); + } + for (p = Glob.usable->first; p; p = p->next) { + if (cac_tautology(p->c->literals)) + to_delete = plist_prepend(to_delete, p->c); + } + for (p = Glob.limbo->first; p; p = p->next) { + if (cac_tautology(p->c->literals)) + to_delete = plist_prepend(to_delete, p->c); + } + for (a = to_delete; a; a = a->next) { + printf("%% back CAC tautology: "); f_clause(a->v); + disable_clause(a->v); + } + zap_plist(to_delete); /* shallow */ } // back_cac_simplify /************* @@ -1506,43 +1792,43 @@ void back_cac_simplify(void) static void disable_to_be_disabled(void) { - if (Glob.desc_to_be_disabled) { - - Plist descendants = NULL; - Plist p; - - sort_clist_by_id(Glob.disabled); - - for (p = Glob.desc_to_be_disabled; p; p = p->next) { - Topform c = p->v; - Plist x = neg_descendants(c,Glob.usable,Glob.sos,Glob.disabled); - descendants = plist_cat(descendants, x); - } - + if (Glob.desc_to_be_disabled) { + + Plist descendants = NULL; + Plist p; + + sort_clist_by_id(Glob.disabled); + + for (p = Glob.desc_to_be_disabled; p; p = p->next) { + Topform c = p->v; + Plist x = neg_descendants(c,Glob.usable,Glob.sos,Glob.disabled); + descendants = plist_cat(descendants, x); + } + #if 1 - { - int n = 0; - printf("\n%% Disable descendants (x means already disabled):\n"); - for (p = descendants; p; p = p->next) { - Topform d = p->v; - printf(" %d%s", d->id, clist_member(d, Glob.disabled) ? "x" : ""); - if (++n % 10 == 0) - printf("\n"); - } - printf("\n"); - } + { + int n = 0; + printf("\n%% Disable descendants (x means already disabled):\n"); + for (p = descendants; p; p = p->next) { + Topform d = p->v; + printf(" %d%s", d->id, clist_member(d, Glob.disabled) ? "x" : ""); + if (++n % 10 == 0) + printf("\n"); + } + printf("\n"); + } #endif - - for (p = descendants; p; p = p->next) { - Topform d = p->v; - if (!clist_member(d, Glob.disabled)) - disable_clause(d); - } - - zap_plist(descendants); - zap_plist(Glob.desc_to_be_disabled); - Glob.desc_to_be_disabled = NULL; - } + + for (p = descendants; p; p = p->next) { + Topform d = p->v; + if (!clist_member(d, Glob.disabled)) + disable_clause(d); + } + + zap_plist(descendants); + zap_plist(Glob.desc_to_be_disabled); + Glob.desc_to_be_disabled = NULL; + } } /* disable_to_be_disabled */ /************* @@ -1566,115 +1852,149 @@ void disable_to_be_disabled(void) static void limbo_process(BOOL pre_search) { - while (Glob.limbo->first) { - Topform c = Glob.limbo->first->c; - - // factoring - - if (flag(Opt->factor)) - binary_factors(c, cl_process); - - // Try to apply new_constant rule. - - if (!at_parm_limit(Stats.new_constants, Opt->new_constants)) { - Topform new = new_constant(c, INT_MAX); - if (new) { - Stats.new_constants++; - if (!flag(Opt->quiet)) { - printf("\nNOTE: New constant: "); - f_clause(new); - printf("NOTE: New "); - print_fsym_precedence(stdout); - } - if (Glob.interps) - update_semantics_new_constant(new); - cl_process(new); - } + while (Glob.limbo->first) { + Topform c = Glob.limbo->first->c; + + //if (flag(Opt->loopdet)) { + //binary_factors(c, cl_process); + //} + + // factoring + + if (flag(Opt->factor)|| (flag(Opt->superind) && !param_free(c)) ){ + binary_factors(c, cl_process); + //printf("W W "); + //p_clause(c); + + } + + // Try to apply new_constant rule. + + if (!at_parm_limit(Stats.new_constants, Opt->new_constants)) { + Topform new = new_constant(c, INT_MAX); + if (new) { + Stats.new_constants++; + if (!flag(Opt->quiet)) { + printf("\nNOTE: New constant: "); + f_clause(new); + printf("NOTE: New "); + print_fsym_precedence(stdout); + } + if (Glob.interps) + update_semantics_new_constant(new); + cl_process(new); + } + } + + // fold denial (for input clauses only) + + if (parm(Opt->fold_denial_max) > 1 && + (has_input_just(c) || has_copy_just(c))) { + Topform new = fold_denial(c, parm(Opt->fold_denial_max)); + if (new) { + if (!flag(Opt->quiet)) { + printf("\nNOTE: Fold denial: "); + f_clause(new); + } + cl_process(new); + } + } + + // Disable clauses subsumed by c (back subsumption). + + if (flag(Opt->back_subsume)) { + Plist subsumees; + clock_start(Clocks.back_subsume); + subsumees = back_subsumption(c); + if (subsumees != NULL) + c->subsumer = TRUE; + while (subsumees != NULL) { + Topform d = subsumees->v; + if (clist_member(d, Glob.limbo) && !pureparam_cst_topform(c)){ // See comment in cl_process.Modif + p_clause(d); + p_clause(c); + fatal_error("back subsume limbo clause"); + } + Stats.back_subsumed++; + if (flag(Opt->print_kept)) + printf(" %d back subsumes %d.\n", c->id, d->id); + disable_clause(d); + subsumees = plist_pop(subsumees); + } + clock_stop(Clocks.back_subsume); + } + + // If demodulator, rewrite other clauses (back demodulation). + + if (clist_member(c, Glob.demods)) { + if (flag(Opt->print_kept)) + printf(" starting back demodulation with %d.\n", c->id); + back_demod(c); // This calls cl_process on rewritable clauses. + } + + // If unit, use it to simplify other clauses (back unit_deletion) + + if (flag(Opt->unit_deletion) && unit_clause(c->literals)) { + back_unit_deletion(c); // This calls cl_process on rewritable clauses. + } + + // Check if we should do back CAC simplification. + + if (plist_member(Glob.cac_clauses, c)) { + back_cac_simplify(); + } + + // Remove from limbo + + clist_remove(c, Glob.limbo); + /**************************************Modif *****************************/ + if(pureparam_cst_topform(c)){ + //printf("th"); + //p_clause(c); + Glob.tab_rank[get_rank(c)]= TRUE; + /*if(Glob.max_rank < get_rank(c)){ + Glob.max_rank = get_rank(c); + + }*/ + //printf("E : ");p_clause(c);printf(" E\n "); + //p_plist(Glob.rank_emptycl); + Glob.rank_emptycl = plist_append(Glob.rank_emptycl, c); + //p_plist(Glob.rank_emptycl); + + } + + /*.....................................................*/ + + // If restricted_denial, appdend to usable, else append to sos. + + if (restricted_denial(c)) { + // do not index_clashable! disable_clause should not unindex_clashable! + clist_append(c, Glob.usable); + index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); + } + else { + // Move to Sos and index to be found for back demodulation. + if (parm(Opt->sos_limit) != -1 && + clist_length(Glob.sos) >= parm(Opt->sos_limit)) { + sos_displace2(disable_clause); + Stats.sos_displaced++; + } + if (pre_search) + c->initial = TRUE; + else + c->initial = FALSE; + insert_into_sos2(c, Glob.sos); + + } + + index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); + + } - - // fold denial (for input clauses only) - - if (parm(Opt->fold_denial_max) > 1 && - (has_input_just(c) || has_copy_just(c))) { - Topform new = fold_denial(c, parm(Opt->fold_denial_max)); - if (new) { - if (!flag(Opt->quiet)) { - printf("\nNOTE: Fold denial: "); - f_clause(new); - } - cl_process(new); - } - } - - // Disable clauses subsumed by c (back subsumption). - - if (flag(Opt->back_subsume)) { - Plist subsumees; - clock_start(Clocks.back_subsume); - subsumees = back_subsumption(c); - if (subsumees != NULL) - c->subsumer = TRUE; - while (subsumees != NULL) { - Topform d = subsumees->v; - if (clist_member(d, Glob.limbo)) // See comment in cl_process. - fatal_error("back subsume limbo clause"); - Stats.back_subsumed++; - if (flag(Opt->print_kept)) - printf(" %d back subsumes %d.\n", c->id, d->id); - disable_clause(d); - subsumees = plist_pop(subsumees); - } - clock_stop(Clocks.back_subsume); - } - - // If demodulator, rewrite other clauses (back demodulation). - - if (clist_member(c, Glob.demods)) { - if (flag(Opt->print_kept)) - printf(" starting back demodulation with %d.\n", c->id); - back_demod(c); // This calls cl_process on rewritable clauses. - } - - // If unit, use it to simplify other clauses (back unit_deletion) - - if (flag(Opt->unit_deletion) && unit_clause(c->literals)) { - back_unit_deletion(c); // This calls cl_process on rewritable clauses. - } - - // Check if we should do back CAC simplification. - - if (plist_member(Glob.cac_clauses, c)) { - back_cac_simplify(); - } - - // Remove from limbo - - clist_remove(c, Glob.limbo); - - // If restricted_denial, appdend to usable, else append to sos. - - if (restricted_denial(c)) { - // do not index_clashable! disable_clause should not unindex_clashable! - clist_append(c, Glob.usable); - index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); - } - else { - // Move to Sos and index to be found for back demodulation. - if (parm(Opt->sos_limit) != -1 && - clist_length(Glob.sos) >= parm(Opt->sos_limit)) { - sos_displace2(disable_clause); - Stats.sos_displaced++; - } - if (pre_search) - c->initial = TRUE; - else - c->initial = FALSE; - insert_into_sos2(c, Glob.sos); - index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); - } - } - // Now it is safe to disable descendants of desc_to_be_disabled clauses. - disable_to_be_disabled(); + + + // Now it is safe to disable descendants of desc_to_be_disabled clauses. + disable_to_be_disabled(); } // limbo_process /************* @@ -1723,51 +2043,51 @@ void infer_outside_loop(Topform c) static void given_infer(Topform given) { - clock_start(Clocks.infer); - - if (flag(Opt->binary_resolution)) - binary_resolution(given, - ANY_RES, - Glob.clashable_idx, - cl_process); - - if (flag(Opt->neg_binary_resolution)) - binary_resolution(given, - NEG_RES, - Glob.clashable_idx, - cl_process); - - if (flag(Opt->pos_hyper_resolution)) - hyper_resolution(given, POS_RES, Glob.clashable_idx, cl_process); - - if (flag(Opt->neg_hyper_resolution)) - hyper_resolution(given, NEG_RES, Glob.clashable_idx, cl_process); - - if (flag(Opt->pos_ur_resolution)) - ur_resolution(given, POS_RES, Glob.clashable_idx, cl_process); - - if (flag(Opt->neg_ur_resolution)) - ur_resolution(given, NEG_RES, Glob.clashable_idx, cl_process); - - if (flag(Opt->paramodulation) && - !over_parm_limit(number_of_literals(given->literals), - Opt->para_lit_limit)) { - // This paramodulation does not use indexing. - Context cf = get_context(); - Context ci = get_context(); - Clist_pos p; - for (p = Glob.usable->first; p; p = p->next) { - if (!restricted_denial(p->c) && - !over_parm_limit(number_of_literals(p->c->literals), - Opt->para_lit_limit)) { - para_from_into(given, cf, p->c, ci, FALSE, cl_process); - para_from_into(p->c, cf, given, ci, TRUE, cl_process); - } - } - free_context(cf); - free_context(ci); - } - clock_stop(Clocks.infer); + clock_start(Clocks.infer); + + if (flag(Opt->binary_resolution)) + binary_resolution(given, + ANY_RES, + Glob.clashable_idx, + cl_process); + + if (flag(Opt->neg_binary_resolution)) + binary_resolution(given, + NEG_RES, + Glob.clashable_idx, + cl_process); + + if (flag(Opt->pos_hyper_resolution)) + hyper_resolution(given, POS_RES, Glob.clashable_idx, cl_process); + + if (flag(Opt->neg_hyper_resolution)) + hyper_resolution(given, NEG_RES, Glob.clashable_idx, cl_process); + + if (flag(Opt->pos_ur_resolution)) + ur_resolution(given, POS_RES, Glob.clashable_idx, cl_process); + + if (flag(Opt->neg_ur_resolution)) + ur_resolution(given, NEG_RES, Glob.clashable_idx, cl_process); + + if (flag(Opt->paramodulation) && + !over_parm_limit(number_of_literals(given->literals), + Opt->para_lit_limit)) { + // This paramodulation does not use indexing. + Context cf = get_context(); + Context ci = get_context(); + Clist_pos p; + for (p = Glob.usable->first; p; p = p->next) { + if (!restricted_denial(p->c) && + !over_parm_limit(number_of_literals(p->c->literals), + Opt->para_lit_limit)) { + para_from_into(given, cf, p->c, ci, FALSE, cl_process); + para_from_into(p->c, cf, given, ci, TRUE, cl_process); + } + } + free_context(cf); + free_context(ci); + } + clock_stop(Clocks.infer); } // given_infer /************* @@ -1805,79 +2125,87 @@ void rebuild_sos_index(void) static void make_inferences(void) -{ - Topform given_clause; - char *selection_type; - - clock_start(Clocks.pick_given); - given_clause = get_given_clause2(Glob.sos,Stats.given, Opt, &selection_type); - clock_stop(Clocks.pick_given); - - if (given_clause != NULL) { - static int level = 0; // NOTE: STATIC VARIABLE - static int last_of_level = 0; // NOTE: STATIC VARIABLE - - // Print "level" message for breadth-first; also "level" actions. - - if (flag(Opt->breadth_first) && - parm(Opt->true_part) == 0 && - parm(Opt->false_part) == 0 && - parm(Opt->weight_part) == 0 && - parm(Opt->random_part) == 0 && - str_ident(selection_type, "A") && - given_clause->id > last_of_level) { - level++; - last_of_level = clause_ids_assigned(); - if (!flag(Opt->quiet)) { - printf("\nNOTE: Starting on level %d, last clause " - "of level %d is %d.\n", - level, level-1, last_of_level); - fflush(stdout); - fprintf(stderr, "\nStarting on level %d, last clause " - "of level %d is %d.\n", - level, level-1, last_of_level); - fflush(stderr); - } - statistic_actions("level", level); - } - - Stats.given++; - - // Maybe disable back subsumption. - - if (over_parm_limit(Stats.given, Opt->max_given)) - done_with_search(MAX_GIVEN_EXIT); - - if (Stats.given == parm(Opt->backsub_check)) { - int ratio = (Stats.back_subsumed == 0 ? - INT_MAX : - Stats.kept / Stats.back_subsumed); - if (ratio > 20) { - clear_flag(Opt->back_subsume, TRUE); - printf("\nNOTE: Back_subsumption disabled, ratio of kept" - " to back_subsumed is %d (%.2f of %.2f sec).\n", - ratio, clock_seconds(Clocks.back_subsume), user_seconds()); - fflush(stdout); - } - } - - if (flag(Opt->print_given)) { - if (given_clause->weight == round(given_clause->weight)) - printf("\ngiven #%d (%s,wt=%d): ", - Stats.given, selection_type, (int) given_clause->weight); - else - printf("\ngiven #%d (%s,wt=%.3f): ", - Stats.given, selection_type, given_clause->weight); - fwrite_clause(stdout, given_clause, CL_FORM_STD); - } - - statistic_actions("given", Stats.given); - - clist_append(given_clause, Glob.usable); - index_clashable(given_clause, INSERT); - given_infer(given_clause); - } -} // make_inferences + { + Topform given_clause; + char *selection_type; + /************************** Modif ************************/ + clock_start(Clocks.pick_given); + given_clause = get_given_clause2(Glob.sos,Stats.given, Opt, &selection_type); + clock_stop(Clocks.pick_given); + + if (given_clause != NULL) { + if(flag(Opt->sat)){ + if (flag(Opt->rank_given) & Glob.admissible) { + if (get_rank(given_clause) > Glob.max_rank + 1) { + handle_proof_and_maybe_exit2(); + } + } + } + static int level = 0; // NOTE: STATIC VARIABLE + static int last_of_level = 0; // NOTE: STATIC VARIABLE + + // Print "level" message for breadth-first; also "level" actions. + + if (flag(Opt->breadth_first) && + parm(Opt->true_part) == 0 && + parm(Opt->false_part) == 0 && + parm(Opt->weight_part) == 0 && + parm(Opt->random_part) == 0 && + parm(Opt->rank_part) == 0 && // Modif + str_ident(selection_type, "A") && + given_clause->id > last_of_level) { + level++; + last_of_level = clause_ids_assigned(); + if (!flag(Opt->quiet)) { + printf("\nNOTE: Starting on level %d, last clause " + "of level %d is %d.\n", + level, level-1, last_of_level); + fflush(stdout); + fprintf(stderr, "\nStarting on level %d, last clause " + "of level %d is %d.\n", + level, level-1, last_of_level); + fflush(stderr); + } + statistic_actions("level", level); + } + + Stats.given++; + + // Maybe disable back subsumption. + + if (over_parm_limit(Stats.given, Opt->max_given)) + done_with_search(MAX_GIVEN_EXIT); + + if (Stats.given == parm(Opt->backsub_check)) { + int ratio = (Stats.back_subsumed == 0 ? + INT_MAX : + Stats.kept / Stats.back_subsumed); + if (ratio > 20) { + clear_flag(Opt->back_subsume, TRUE); + printf("\nNOTE: Back_subsumption disabled, ratio of kept" + " to back_subsumed is %d (%.2f of %.2f sec).\n", + ratio, clock_seconds(Clocks.back_subsume), user_seconds()); + fflush(stdout); + } + } + + if (flag(Opt->print_given)) { + if (given_clause->weight == round(given_clause->weight)) + printf("\ngiven #%d (%s,wt=%d , Rk = %d): ", + Stats.given, selection_type, (int) given_clause->weight, get_rank(given_clause)); + else + printf("\ngiven #%d (%s,wt=%.3f): ", + Stats.given, selection_type, given_clause->weight); + fwrite_clause(stdout, given_clause, CL_FORM_STD); + } + + statistic_actions("given", Stats.given); + + clist_append(given_clause, Glob.usable); + index_clashable(given_clause, INSERT); + given_infer(given_clause); + } + } // make_inferences /************* * @@ -2100,427 +2428,427 @@ void auto_denials(Clist sos, Clist usable, Prover_options opt) static void init_search(void) -{ - // Initialize clocks. - - Clocks.pick_given = clock_init("pick_given"); - Clocks.infer = clock_init("infer"); - Clocks.preprocess = clock_init("preprocess"); - Clocks.demod = clock_init("demod"); - Clocks.unit_del = clock_init("unit_deletion"); - Clocks.redundancy = clock_init("redundancy"); - Clocks.conflict = clock_init("conflict"); - Clocks.weigh = clock_init("weigh"); - Clocks.hints = clock_init("hints"); - Clocks.subsume = clock_init("subsume"); - Clocks.semantics = clock_init("semantics"); - Clocks.back_subsume = clock_init("back_subsume"); - Clocks.back_demod = clock_init("back_demod"); - Clocks.back_unit_del = clock_init("back_unit_del"); - Clocks.index = clock_init("index"); - Clocks.disable = clock_init("disable"); - - init_actions(Glob.actions, - rebuild_sos_index, done_with_search, infer_outside_loop); - init_weight(Glob.weights, - floatparm(Opt->variable_weight), - floatparm(Opt->constant_weight), - floatparm(Opt->not_weight), - floatparm(Opt->or_weight), - floatparm(Opt->sk_constant_weight), - floatparm(Opt->prop_atom_weight), - floatparm(Opt->nest_penalty), - floatparm(Opt->depth_penalty), - floatparm(Opt->var_penalty), - floatparm(Opt->complexity)); - - if (Glob.given_selection == NULL) - Glob.given_selection = selector_rules_from_options(Opt); - else if (flag(Opt->input_sos_first)) - Glob.given_selection = plist_prepend(Glob.given_selection, - selector_rule_term("I", "high", "age", - "initial", - INT_MAX)); - init_giv_select(Glob.given_selection); - - Glob.delete_rules = plist_cat(delete_rules_from_options(Opt), - Glob.delete_rules); - - init_white_black(Glob.keep_rules, Glob.delete_rules); - - // Term ordering - - printf("\nTerm ordering decisions:\n"); - - if (stringparm(Opt->order, "lpo")) { - assign_order_method(LPO_METHOD); - all_symbols_lrpo_status(LRPO_LR_STATUS); - set_lrpo_status(str_to_sn(eq_sym(), 2), LRPO_MULTISET_STATUS); - } - else if (stringparm(Opt->order, "rpo")) { - assign_order_method(RPO_METHOD); - all_symbols_lrpo_status(LRPO_MULTISET_STATUS); - } - else if (stringparm(Opt->order, "kbo")) { - assign_order_method(KBO_METHOD); - } - - symbol_order(Glob.usable, Glob.sos, Glob.demods, TRUE); - - if (Glob.kbo_weights) { - if (!stringparm(Opt->order, "kbo")) { - assign_stringparm(Opt->order, "kbo", TRUE); - printf("assign(order, kbo), because KB weights were given.\n"); - } - init_kbo_weights(Glob.kbo_weights); - print_kbo_weights(stdout); - } - else if (stringparm(Opt->order, "kbo")) { - auto_kbo_weights(Glob.usable, Glob.sos); - print_kbo_weights(stdout); - } - - if (!flag(Opt->quiet)) { - print_rsym_precedence(stdout); - print_fsym_precedence(stdout); - } - - if (flag(Opt->inverse_order)) { - if (exists_preliminary_precedence(FUNCTION_SYMBOL)) { // lex command - if (!flag(Opt->quiet)) - printf("Skipping inverse_order, because there is a function_order (lex) command.\n"); - } - else if (stringparm(Opt->order, "kbo")) { - if (!flag(Opt->quiet)) - printf("Skipping inverse_order, because term ordering is KBO.\n"); - } - else { - BOOL change = inverse_order(Glob.sos); - if (!flag(Opt->quiet)) { - printf("After inverse_order: "); - if (change) - print_fsym_precedence(stdout); - else - printf(" (no changes).\n"); - } - } - } - - if (stringparm(Opt->eq_defs, "unfold")) { - if (exists_preliminary_precedence(FUNCTION_SYMBOL)) // lex command - printf("Skipping unfold_eq, because there is a function_order (lex) command.\n"); - else - unfold_eq_defs(Glob.sos, INT_MAX, 3, !flag(Opt->quiet)); - } - else if (stringparm(Opt->eq_defs, "fold")) { - if (exists_preliminary_precedence(FUNCTION_SYMBOL)) // lex command - printf("Skipping fold_eq, because there is a function_order (lex) command.\n"); - else { - BOOL change = fold_eq_defs(Glob.sos, stringparm(Opt->order, "kbo")); - if (!flag(Opt->quiet)) { - printf("After fold_eq: "); - if (change) - print_fsym_precedence(stdout); - else - printf(" (no changes).\n"); - } - } - } - - // Automatic inference and processing settings - - if (flag(Opt->auto_inference)) - auto_inference(Glob.sos, Glob.usable, Opt); - - if (flag(Opt->auto_process)) - auto_process(Glob.sos, Glob.usable, Opt); - - // Tell packages about options and other things. - - resolution_options(flag(Opt->ordered_res), - flag(Opt->check_res_instances), - flag(Opt->initial_nuclei), - parm(Opt->ur_nucleus_limit), - flag(Opt->eval_rewrite)); - - paramodulation_options(flag(Opt->ordered_para), - flag(Opt->check_para_instances), - FALSE, - flag(Opt->basic_paramodulation), - flag(Opt->para_from_vars), - flag(Opt->para_into_vars), - flag(Opt->para_from_small)); - -} /* init_search */ + { + // Initialize clocks. + + Clocks.pick_given = clock_init("pick_given"); + Clocks.infer = clock_init("infer"); + Clocks.preprocess = clock_init("preprocess"); + Clocks.demod = clock_init("demod"); + Clocks.unit_del = clock_init("unit_deletion"); + Clocks.redundancy = clock_init("redundancy"); + Clocks.conflict = clock_init("conflict"); + Clocks.weigh = clock_init("weigh"); + Clocks.hints = clock_init("hints"); + Clocks.subsume = clock_init("subsume"); + Clocks.semantics = clock_init("semantics"); + Clocks.back_subsume = clock_init("back_subsume"); + Clocks.back_demod = clock_init("back_demod"); + Clocks.back_unit_del = clock_init("back_unit_del"); + Clocks.index = clock_init("index"); + Clocks.disable = clock_init("disable"); + + init_actions(Glob.actions, + rebuild_sos_index, done_with_search, infer_outside_loop); + init_weight(Glob.weights, + floatparm(Opt->variable_weight), + floatparm(Opt->constant_weight), + floatparm(Opt->not_weight), + floatparm(Opt->or_weight), + floatparm(Opt->sk_constant_weight), + floatparm(Opt->prop_atom_weight), + floatparm(Opt->nest_penalty), + floatparm(Opt->depth_penalty), + floatparm(Opt->var_penalty), + floatparm(Opt->complexity)); + + if (Glob.given_selection == NULL) + Glob.given_selection = selector_rules_from_options(Opt); + else if (flag(Opt->input_sos_first)) + Glob.given_selection = plist_prepend(Glob.given_selection, + selector_rule_term("I", "high", "age", + "initial", + INT_MAX)); + init_giv_select(Glob.given_selection); + + Glob.delete_rules = plist_cat(delete_rules_from_options(Opt), + Glob.delete_rules); + + init_white_black(Glob.keep_rules, Glob.delete_rules); + + // Term ordering + + printf("\nTerm ordering decisions:\n"); + + if (stringparm(Opt->order, "lpo")) { + assign_order_method(LPO_METHOD); + all_symbols_lrpo_status(LRPO_LR_STATUS); + set_lrpo_status(str_to_sn(eq_sym(), 2), LRPO_MULTISET_STATUS); + } + else if (stringparm(Opt->order, "rpo")) { + assign_order_method(RPO_METHOD); + all_symbols_lrpo_status(LRPO_MULTISET_STATUS); + } + else if (stringparm(Opt->order, "kbo")) { + assign_order_method(KBO_METHOD); + } + + symbol_order(Glob.usable, Glob.sos, Glob.demods, TRUE); + + if (Glob.kbo_weights) { + if (!stringparm(Opt->order, "kbo")) { + assign_stringparm(Opt->order, "kbo", TRUE); + printf("assign(order, kbo), because KB weights were given.\n"); + } + init_kbo_weights(Glob.kbo_weights); + print_kbo_weights(stdout); + } + else if (stringparm(Opt->order, "kbo")) { + auto_kbo_weights(Glob.usable, Glob.sos); + print_kbo_weights(stdout); + } + + if (!flag(Opt->quiet)) { + print_rsym_precedence(stdout); + print_fsym_precedence(stdout); + } + + if (flag(Opt->inverse_order)) { + if (exists_preliminary_precedence(FUNCTION_SYMBOL)) { // lex command + if (!flag(Opt->quiet)) + printf("Skipping inverse_order, because there is a function_order (lex) command.\n"); + } + else if (stringparm(Opt->order, "kbo")) { + if (!flag(Opt->quiet)) + printf("Skipping inverse_order, because term ordering is KBO.\n"); + } + else { + BOOL change = inverse_order(Glob.sos); + if (!flag(Opt->quiet)) { + printf("After inverse_order: "); + if (change) + print_fsym_precedence(stdout); + else + printf(" (no changes).\n"); + } + } + } + + if (stringparm(Opt->eq_defs, "unfold")) { + if (exists_preliminary_precedence(FUNCTION_SYMBOL)) // lex command + printf("Skipping unfold_eq, because there is a function_order (lex) command.\n"); + else + unfold_eq_defs(Glob.sos, INT_MAX, 3, !flag(Opt->quiet)); + } + else if (stringparm(Opt->eq_defs, "fold")) { + if (exists_preliminary_precedence(FUNCTION_SYMBOL)) // lex command + printf("Skipping fold_eq, because there is a function_order (lex) command.\n"); + else { + BOOL change = fold_eq_defs(Glob.sos, stringparm(Opt->order, "kbo")); + if (!flag(Opt->quiet)) { + printf("After fold_eq: "); + if (change) + print_fsym_precedence(stdout); + else + printf(" (no changes).\n"); + } + } + } + + // Automatic inference and processing settings + + if (flag(Opt->auto_inference)) + auto_inference(Glob.sos, Glob.usable, Opt); + + if (flag(Opt->auto_process)) + auto_process(Glob.sos, Glob.usable, Opt); + + // Tell packages about options and other things. + + resolution_options(flag(Opt->ordered_res), + flag(Opt->check_res_instances), + flag(Opt->initial_nuclei), + parm(Opt->ur_nucleus_limit), + flag(Opt->eval_rewrite)); + + paramodulation_options(flag(Opt->ordered_para), + flag(Opt->check_para_instances), + FALSE, + flag(Opt->basic_paramodulation), + flag(Opt->para_from_vars), + flag(Opt->para_into_vars), + flag(Opt->para_from_small)); + + } /* init_search */ /************* * * index_and_process_initial_clauses() * *************/ - -static -void index_and_process_initial_clauses(void) -{ - Clist_pos p; - Clist temp_sos; - - // Index Usable clauses if hyper, UR, or binary-res are set. - - Glob.use_clash_idx = (flag(Opt->binary_resolution) || - flag(Opt->neg_binary_resolution) || - flag(Opt->pos_hyper_resolution) || - flag(Opt->neg_hyper_resolution) || - flag(Opt->pos_ur_resolution) || - flag(Opt->neg_ur_resolution)); - - // Allocate and initialize indexes (even if they won't be used). - - init_literals_index(); // fsub, bsub, fudel, budel, ucon - - init_demodulator_index(DISCRIM_BIND, ORDINARY_UNIF, 0); - - init_back_demod_index(FPA, ORDINARY_UNIF, 10); - - Glob.clashable_idx = lindex_init(FPA, ORDINARY_UNIF, 10, - FPA, ORDINARY_UNIF, 10); - - init_hints(ORDINARY_UNIF, Att.bsub_hint_wt, - flag(Opt->collect_hint_labels), - flag(Opt->back_demod_hints), - demodulate_clause); - init_semantics(Glob.interps, Clocks.semantics, - stringparm1(Opt->multiple_interps), - parm(Opt->eval_limit), - parm(Opt->eval_var_limit)); - - // Do Sos and Denials last, in case we PROCESS_INITIAL_SOS. - - //////////////////////////////////////////////////////////////////////////// - // Usable - - for (p = Glob.usable->first; p != NULL; p = p->next) { - Topform c = p->c; - assign_clause_id(c); - mark_maximal_literals(c->literals); - mark_selected_literals(c->literals, stringparm1(Opt->literal_selection)); - if (flag(Opt->dont_flip_input)) - orient_equalities(c, FALSE); // mark, but don't allow flips - else - c = orient_input_eq(c); /* this replaces c if any flipping occurs */ - index_literals(c, INSERT, Clocks.index, FALSE); - index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); - index_clashable(c, INSERT); - } - - //////////////////////////////////////////////////////////////////////////// - // Demodulators - - if (!clist_empty(Glob.demods) && !flag(Opt->eval_rewrite)) { - fflush(stdout); - bell(stderr); - fprintf(stderr, - "\nWARNING: The use of input demodulators is not well tested\n" - "and discouraged. You might need to clear(process_initial_sos)\n" - "so that sos clauses are not rewritten and deleted.\n"); - fflush(stderr); - } - - for (p = Glob.demods->first; p != NULL; p = p->next) { - Topform c = p->c; - assign_clause_id(c); - if (flag(Opt->eval_rewrite)) { - if (c->is_formula) { - /* make it into a pseudo-clause */ - c->literals = new_literal(TRUE, formula_to_term(c->formula)); - upward_clause_links(c); - zap_formula(c->formula); - c->formula = NULL; - c->is_formula = FALSE; - clause_set_variables(c, MAX_VARS); - mark_oriented_eq(c->literals->atom); - } - } - else { - if (!pos_eq_unit(c->literals)) - fatal_error("input demodulator is not equation"); - else { - int type; - if (flag(Opt->dont_flip_input)) - orient_equalities(c, FALSE); /* don't allow flips */ - else - c = orient_input_eq(c); /* this replaces c if any flipping occurs */ - if (c->justification->next != NULL) { - printf("\nNOTE: input demodulator %d has been flipped.\n", c->id); - fflush(stdout); - fprintf(stderr, "\nNOTE: input demodulator %d has been flipped.\n", - c->id); - if (flag(Opt->bell)) - bell(stderr); - fflush(stderr); - } - type = demodulator_type(c, - parm(Opt->lex_dep_demod_lim), - flag(Opt->lex_dep_demod_sane)); - if (flag(Opt->dont_flip_input) && - type != ORIENTED && - !renamable_flip_eq(c->literals->atom)) { - type = ORIENTED; /* let the user beware */ - mark_oriented_eq(c->literals->atom); - bell(stderr); - fprintf(stderr,"\nWARNING: demodulator does not satisfy term order\n"); - fflush(stderr); - printf("\nWARNING: demodulator does not satisfy term order: "); - f_clause(c); - fflush(stdout); - } - else if (type == NOT_DEMODULATOR) { - Term a = ARG(c->literals->atom,0); - Term b = ARG(c->literals->atom,1); - printf("bad input demodulator: "); f_clause(c); - if (term_ident(a, b)) - fatal_error("input demodulator is instance of x=x"); - else if (!variables_subset(a, b) && !variables_subset(b, a)) - fatal_error("input demoulator does not have var-subset property"); - else - fatal_error("input demoulator not allowed"); - } - index_demodulator(c, type, INSERT, Clocks.index); - } - } - } - - if (flag(Opt->eval_rewrite)) - init_dollar_eval(Glob.demods); - - //////////////////////////////////////////////////////////////////////////// - // Hints - - if (Glob.hints->first) { - for (p = Glob.hints->first; p != NULL; p = p->next) { - Topform h = p->c; - // assign_clause_id(h); // This should be optional - orient_equalities(h, TRUE); - renumber_variables(h, MAX_VARS); - index_hint(h); - } - } - - //////////////////////////////////////////////////////////////////////////// - // Sos - - // Move Sos to a temporary list, then process that temporary list, - // putting the clauses back into Sos in the "correct" way, either - // by calling cl_process() or doing it here. - - temp_sos = Glob.sos; // move Sos to a temporary list - name_clist(temp_sos, "temp_sos"); // not really necessary - Glob.sos = clist_init("sos"); // get a new (empty) Sos list - - if (flag(Opt->process_initial_sos)) { - - if (flag(Opt->print_initial_clauses)) - printf("\n"); - - while (temp_sos->first) { - Topform c = temp_sos->first->c; - Topform new; - clist_remove(c, temp_sos); - clist_append(c, Glob.disabled); - - new = copy_inference(c); // c has no ID, so this is tricky - cl_process_simplify(new); - if (new->justification->next == NULL) { - // No simplification occurred, so make it a clone of the parent. - zap_just(new->justification); - new->justification = copy_justification(c->justification); - // Get all attributes, not just inheritable ones. - zap_attributes(new->attributes); - new->attributes = copy_attributes(c->attributes); - } - else { - // Simplification occurs, so make it a child of the parent. - assign_clause_id(c); - new->justification->u.id = c->id; - if (flag(Opt->print_initial_clauses)) { - printf(" "); - fwrite_clause(stdout, c, CL_FORM_STD); - } - } - cl_process(new); // This re-simplifies, but that's ok. - } - // This will put processed clauses back into Sos. - limbo_process(TRUE); // back subsumption and back demodulation. - - } - else { - /* not processing initial sos */ - fflush(stdout); - bell(stderr); - fprintf(stderr, - "\nWARNING: clear(process_initial_sos) is not well tested.\n" - "We usually recommend against using it.\n"); - fflush(stderr); - - /* not applying full processing to initial sos */ - while (temp_sos->first) { - Topform c = temp_sos->first->c; - clist_remove(c, temp_sos); - - if (number_of_literals(c->literals) == 0) - /* in case $F is in input, or if predicate elimination finds proof */ - handle_proof_and_maybe_exit(c); - else { - assign_clause_id(c); - if (flag(Opt->dont_flip_input)) - orient_equalities(c, FALSE); - else - c = orient_input_eq(c); - mark_maximal_literals(c->literals); - mark_selected_literals(c->literals, - stringparm1(Opt->literal_selection)); - c->weight = clause_weight(c->literals); - if (!clist_empty(Glob.hints)) { - clock_start(Clocks.hints); - adjust_weight_with_hints(c, - flag(Opt->degrade_hints), - flag(Opt->breadth_first_hints)); - clock_stop(Clocks.hints); - } - - c->initial = TRUE; - insert_into_sos2(c, Glob.sos); - index_literals(c, INSERT, Clocks.index, FALSE); - index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); - } - } - } - - clist_zap(temp_sos); // free the temporary list - - //////////////////////////////////////////////////////////////////////////// - // Print - - print_separator(stdout, "end of process initial clauses", TRUE); - - print_separator(stdout, "CLAUSES FOR SEARCH", TRUE); - - if (flag(Opt->print_initial_clauses)) { - printf("\n%% Clauses after input processing:\n"); - fwrite_clause_clist(stdout,Glob.usable, CL_FORM_STD); - fwrite_clause_clist(stdout,Glob.sos, CL_FORM_STD); - fwrite_demod_clist(stdout,Glob.demods, CL_FORM_STD); - } - if (Glob.hints->length > 0) { - int redundant = redundant_hints(); - printf("\n%% %d hints (%d processed, %d redundant).\n", - Glob.hints->length - redundant, Glob.hints->length, redundant); - } - - print_separator(stdout, "end of clauses for search", TRUE); - -} // index_and_process_initial_clauses - + static + void index_and_process_initial_clauses(void) + { + Clist_pos p; + Clist temp_sos; + + // Index Usable clauses if hyper, UR, or binary-res are set. + + Glob.use_clash_idx = (flag(Opt->binary_resolution) || + flag(Opt->neg_binary_resolution) || + flag(Opt->pos_hyper_resolution) || + flag(Opt->neg_hyper_resolution) || + flag(Opt->pos_ur_resolution) || + flag(Opt->neg_ur_resolution)); + + // Allocate and initialize indexes (even if they won't be used). + + init_literals_index(); // fsub, bsub, fudel, budel, ucon + + init_demodulator_index(DISCRIM_BIND, ORDINARY_UNIF, 0); + + init_back_demod_index(FPA, ORDINARY_UNIF, 10); + + Glob.clashable_idx = lindex_init(FPA, ORDINARY_UNIF, 10, + FPA, ORDINARY_UNIF, 10); + + init_hints(ORDINARY_UNIF, Att.bsub_hint_wt, + flag(Opt->collect_hint_labels), + flag(Opt->back_demod_hints), + demodulate_clause); + init_semantics(Glob.interps, Clocks.semantics, + stringparm1(Opt->multiple_interps), + parm(Opt->eval_limit), + parm(Opt->eval_var_limit)); + + // Do Sos and Denials last, in case we PROCESS_INITIAL_SOS. + + //////////////////////////////////////////////////////////////////////////// + // Usable + + for (p = Glob.usable->first; p != NULL; p = p->next) { + Topform c = p->c; + assign_clause_id(c); + mark_maximal_literals(c->literals); + mark_selected_literals(c->literals, stringparm1(Opt->literal_selection)); + if (flag(Opt->dont_flip_input)) + orient_equalities(c, FALSE); // mark, but don't allow flips + else + c = orient_input_eq(c); /* this replaces c if any flipping occurs */ + index_literals(c, INSERT, Clocks.index, FALSE); + index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); + index_clashable(c, INSERT); + } + + //////////////////////////////////////////////////////////////////////////// + // Demodulators + + if (!clist_empty(Glob.demods) && !flag(Opt->eval_rewrite)) { + fflush(stdout); + bell(stderr); + fprintf(stderr, + "\nWARNING: The use of input demodulators is not well tested\n" + "and discouraged. You might need to clear(process_initial_sos)\n" + "so that sos clauses are not rewritten and deleted.\n"); + fflush(stderr); + } + + for (p = Glob.demods->first; p != NULL; p = p->next) { + Topform c = p->c; + assign_clause_id(c); + if (flag(Opt->eval_rewrite)) { + if (c->is_formula) { + /* make it into a pseudo-clause */ + c->literals = new_literal(TRUE, formula_to_term(c->formula)); + upward_clause_links(c); + zap_formula(c->formula); + c->formula = NULL; + c->is_formula = FALSE; + clause_set_variables(c, MAX_VARS); + mark_oriented_eq(c->literals->atom); + } + } + else { + if (!pos_eq_unit(c->literals)) + fatal_error("input demodulator is not equation"); + else { + int type; + if (flag(Opt->dont_flip_input)) + orient_equalities(c, FALSE); /* don't allow flips */ + else + c = orient_input_eq(c); /* this replaces c if any flipping occurs */ + if (c->justification->next != NULL) { + printf("\nNOTE: input demodulator %d has been flipped.\n", c->id); + fflush(stdout); + fprintf(stderr, "\nNOTE: input demodulator %d has been flipped.\n", + c->id); + if (flag(Opt->bell)) + bell(stderr); + fflush(stderr); + } + type = demodulator_type(c, + parm(Opt->lex_dep_demod_lim), + flag(Opt->lex_dep_demod_sane)); + if (flag(Opt->dont_flip_input) && + type != ORIENTED && + !renamable_flip_eq(c->literals->atom)) { + type = ORIENTED; /* let the user beware */ + mark_oriented_eq(c->literals->atom); + bell(stderr); + fprintf(stderr,"\nWARNING: demodulator does not satisfy term order\n"); + fflush(stderr); + printf("\nWARNING: demodulator does not satisfy term order: "); + f_clause(c); + fflush(stdout); + } + else if (type == NOT_DEMODULATOR) { + Term a = ARG(c->literals->atom,0); + Term b = ARG(c->literals->atom,1); + printf("bad input demodulator: "); f_clause(c); + if (term_ident(a, b)) + fatal_error("input demodulator is instance of x=x"); + else if (!variables_subset(a, b) && !variables_subset(b, a)) + fatal_error("input demoulator does not have var-subset property"); + else + fatal_error("input demoulator not allowed"); + } + index_demodulator(c, type, INSERT, Clocks.index); + } + } + } + + if (flag(Opt->eval_rewrite)) + init_dollar_eval(Glob.demods); + + //////////////////////////////////////////////////////////////////////////// + // Hints + + if (Glob.hints->first) { + for (p = Glob.hints->first; p != NULL; p = p->next) { + Topform h = p->c; + // assign_clause_id(h); // This should be optional + orient_equalities(h, TRUE); + renumber_variables(h, MAX_VARS); + index_hint(h); + } + } + + //////////////////////////////////////////////////////////////////////////// + // Sos + + // Move Sos to a temporary list, then process that temporary list, + // putting the clauses back into Sos in the "correct" way, either + // by calling cl_process() or doing it here. + + temp_sos = Glob.sos; // move Sos to a temporary list + name_clist(temp_sos, "temp_sos"); // not really necessary + Glob.sos = clist_init("sos"); // get a new (empty) Sos list + + if (flag(Opt->process_initial_sos)) { + + if (flag(Opt->print_initial_clauses)) + printf("\n"); + + while (temp_sos->first) { + Topform c = temp_sos->first->c; + Topform new; + clist_remove(c, temp_sos); + clist_append(c, Glob.disabled); + + new = copy_inference(c); // c has no ID, so this is tricky + cl_process_simplify(new); + if (new->justification->next == NULL) { + // No simplification occurred, so make it a clone of the parent. + zap_just(new->justification); + new->justification = copy_justification(c->justification); + // Get all attributes, not just inheritable ones. + zap_attributes(new->attributes); + new->attributes = copy_attributes(c->attributes); + } + else { + // Simplification occurs, so make it a child of the parent. + assign_clause_id(c); + new->justification->u.id = c->id; + if (flag(Opt->print_initial_clauses)) { + printf(" "); + fwrite_clause(stdout, c, CL_FORM_STD); + } + } + cl_process(new); // This re-simplifies, but that's ok. + } + // This will put processed clauses back into Sos. + limbo_process(TRUE); // back subsumption and back demodulation. + + } + else { + /* not processing initial sos */ + fflush(stdout); + bell(stderr); + fprintf(stderr, + "\nWARNING: clear(process_initial_sos) is not well tested.\n" + "We usually recommend against using it.\n"); + fflush(stderr); + + /* not applying full processing to initial sos */ + while (temp_sos->first) { + Topform c = temp_sos->first->c; + clist_remove(c, temp_sos); + + if (number_of_literals(c->literals) == 0) + /* in case $F is in input, or if predicate elimination finds proof */ + handle_proof_and_maybe_exit(c); + else { + assign_clause_id(c); + if (flag(Opt->dont_flip_input)) + orient_equalities(c, FALSE); + else + c = orient_input_eq(c); + mark_maximal_literals(c->literals); + mark_selected_literals(c->literals, + stringparm1(Opt->literal_selection)); + c->weight = clause_weight(c->literals); + if (!clist_empty(Glob.hints)) { + clock_start(Clocks.hints); + adjust_weight_with_hints(c, + flag(Opt->degrade_hints), + flag(Opt->breadth_first_hints)); + clock_stop(Clocks.hints); + } + + c->initial = TRUE; + insert_into_sos2(c, Glob.sos); + index_literals(c, INSERT, Clocks.index, FALSE); + index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); + } + } + } + + clist_zap(temp_sos); // free the temporary list + + //////////////////////////////////////////////////////////////////////////// + // Print + + print_separator(stdout, "end of process initial clauses", TRUE); + + print_separator(stdout, "CLAUSES FOR SEARCH", TRUE); + + if (flag(Opt->print_initial_clauses)) { + printf("\n%% Clauses after input processing:\n"); + fwrite_clause_clist(stdout,Glob.usable, CL_FORM_STD); + fwrite_clause_clist(stdout,Glob.sos, CL_FORM_STD); + fwrite_demod_clist(stdout,Glob.demods, CL_FORM_STD); + } + if (Glob.hints->length > 0) { + int redundant = redundant_hints(); + printf("\n%% %d hints (%d processed, %d redundant).\n", + Glob.hints->length - redundant, Glob.hints->length, redundant); + } + + print_separator(stdout, "end of clauses for search", TRUE); + + } // index_and_process_initial_clauses + + /************* * * fatal_setjmp() @@ -2563,6 +2891,39 @@ Prover_results collect_prover_results(BOOL xproofs) results->return_code = Glob.return_code; return results; } /* collect_prover_results */ + + + + + /************* + * + * collect_prover_results2() + * + *************/ + + static + Prover_results collect_prover_results2(BOOL xproofs) + { + Plist p; + Prover_results results = calloc(1, sizeof(struct prover_results)); + + /*for (p = Glob.empties; p; p = p->next) { + Plist proof = get_clause_ancestors(p->v); + uncompress_clauses(proof); + results->proofs = plist_append(results->proofs, proof); + if (xproofs) { + Plist xproof = proof_to_xproof(proof); + results->xproofs = plist_append(results->xproofs, xproof); + } + }*/ + results->xproofs = Glob.SI; + update_stats(); /* puts package stats into Stats */ + results->stats = Stats; /* structure copy */ + results->user_seconds = user_seconds(); + results->system_seconds = system_seconds(); + results->return_code = Glob.return_code; + return results; + } /* collect_prover_results2 */ /************* * @@ -2624,7 +2985,232 @@ void basic_clause_properties(Clist sos, Clist usable) zap_plist(sos_temp); zap_plist(usable_temp); } /* basic_clause_properties */ + +/*************************************************** Modif **************************** */ + /************* + * + * fixed_point2() + * + *************/ + // implement the fixed point algorithm cycle2 + + BOOL fixed_point2(int I, int J, Plist Si, Plist Sij, Plist ancestors_of_EmptyCl){ + Plist tmp, ancestor,t; + BOOL B = FALSE; + //printf(" A "); + if ( isEmpty(Si) || isEmpty(Sij)) { + //if ((!(generates(I, Si, Sij)) || isEmpty(Si)) || isEmpty(Sij)) { + //printf(" Sij is not generated by Si \n"); + //printf("isEmpty(Si) = %d \n", isEmpty(Si)); + //printf("isEmpty(Sij) = %d \n", isEmpty(Sij)); + //p_plist(Si); + //p_plist(Sij); + return FALSE; + } + else { + + Topform Ci = find_notsubsumedcl(Si, Sij, J); + //Topform Ci = find_notequalcl(Si, Sij, J); + //printf("T0");p_clause(Ci);printf("T1"); + //Topform Ci = unshift(Cij); + //printf("QQ"); + if (Ci == NULL || pureparam_cst_topform(Ci)){ + //printf("OOO"); + //printf(" FSI = ");p_plist(Si); + //printf(" FSIJ = ");p_plist(Sij); + for (tmp = Sij; tmp; tmp = tmp->next) { + B=FALSE; + for (t = Si; t; t = t->next) { + Topform cpij = shift_cl(t->v, J); + if(clause_ident_order(tmp->v,cpij)) + { + B = TRUE; + } + } + if(!B) { + + Sij=plist_remove_clause(Sij, tmp->v); + + } + //printf(" ZO ");p_plist(ancestor);printf(" Z1 \n"); + } + + Glob.SI = Si; + Glob.SIJ = Sij; + + return TRUE; + } + else{ + + Si=plist_remove_clause(Si, Ci); + //printf(" KO ");p_clause(Ci);printf(" K1 \n"); + if (plist_member_clause(ancestors_of_EmptyCl, Ci)) { + //p_plist(ancestors_of_EmptyCl); + //printf("F %d F", generates1(Si,)); + //p_clause(Ci); + //printf("coucou2"); + return FALSE; + } + + + else { + //printf("Si");p_plist(Si);p_plist(Sij);printf("Sij"); + + for (tmp = Sij; tmp; tmp = tmp->next) { + B=FALSE; + if (is_ancestor(I,Ci,tmp->v)) { + Sij=plist_remove_clause(Sij, tmp->v); + } + + } + return fixed_point2(I, J, Si, Sij, ancestors_of_EmptyCl); + } + } + + } + + } + + + +/*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++*/ + /************* + * + * fixed_point1() + * + *************/ + // implement the fixed point algorithm cycle1. + + BOOL fixed_point1(int I, int J, Plist Sinit, Plist Sloop, Plist Sij, BOOL index_flat){ + Plist tmp,Sitmp,p,tmp0; + Topform Cij,C,t; + BOOL B = TRUE; + BOOL exists_shift = TRUE; + Sitmp = NULL; + Plist Slooptmp = NULL; + //printf("S1i ");p_plist(Sinit); + //printf("S1ij ");p_plist(Sloop); + int Isij, Isi; + Isij = plist_count(Sij); + Isi = plist_count(Sinit); + if (Isi > Isij) { + return FALSE; + } + if ( isEmpty(Sinit) || isEmpty(Sij)) { + return FALSE; + } + else { + //printf("S2i ");p_plist(Sinit); + //printf("S2ij ");p_plist(Sloop); + //Cij = shift_equal(I,J,Si,Sij); + p = Sinit; + while ( p && exists_shift) { + t = (Topform)p->v; + //printf(" t = ");p_clause(t);printf(" false = ");printf("%d",false_clause(t->literals)); + if (t == NULL || false_clause(t->literals)) { + //printf(" false = ");p_clause(t); + Sinit=plist_remove_clause(Sinit, t); + p = p->next; + } + else { + C = shift_cl(t, J); + //printf("C "); p_clause(Cij); + Cij = plist_member_clause_shift(Sij, C); + //printf("Cij "); p_clause(Cij); + if (Cij != NULL) { + if(!plist_member_clause(Sloop, Cij)){ + //printf("S2i ");p_plist(Sinit); + //printf("S2ij ");p_plist(Sloop); + //printf("Cij1 "); p_clause(Cij); + + tmp = get_clause_ancestors_ofrank2(Cij, I,index_flat); + //printf("tmp ");p_plist(tmp); + tmp0 = plist_subtract(tmp, Sitmp); + Sitmp = plist_cat(tmp0, Sitmp); + //printf("Sitmp ");p_plist(Sitmp); + Slooptmp=plist_prepend(Slooptmp, Cij); + //printf("Slooptmp ");p_plist(Slooptmp); + B=FALSE; + } + p = p->next; + } + else { + //printf("SS"); + exists_shift = FALSE; + + + } + } + + + } + if (!exists_shift) { + printf(" This clause has not a shift in S_loop : "); + //p_clause(t); + return FALSE; + } + + if (B) { + Glob.SI = Sinit; + Glob.SIJ = Sloop; + printf("+++++++ Cycle detected +++++++++"); + return TRUE; + } + else { + + Sloop = plist_cat(Slooptmp, Sloop); + Sitmp = plist_subtract(Sitmp, Sinit); + Sinit = plist_cat(Sinit, Sitmp); + //printf("Sinit ");p_plist(Sinit); + return fixed_point1(I,J,Sinit,Sloop,Sij,index_flat); + } + + + + } + } +/*....................................................*/ + BOOL fixed_point(int I, int J, Clist sos, Clist usable){ + Glob.number_of_calls++; + Ilist Tested_EmptyCl = NULL; + Plist tmp,p; + Plist p1 = copy_clist_to_plist_shallow(sos); + Plist p2 = copy_clist_to_plist_shallow(usable); + Plist all_clauses = plist_cat(p1, p2); + Plist Sloop = NULL; + Plist Sij=look_by_rank2(all_clauses, J,flag(Opt->index_flat)); + //BOOL index_flat = TRUE; + Plist EmptyCl = level_empty_clause2(Glob.rank_emptycl, I, J); + //printf("EmptyCl ");p_plist(EmptyCl); + Plist Ancestors = get_ancestors_of_rank2(I,EmptyCl,flag(Opt->index_flat)); + //printf("Si ");p_plist(Ancestors); + BOOL Done = TRUE; + + if (flag(Opt->cycle1)) { + printf("============= Cycle1 ============\n "); + Ancestors = plist_subtract(Ancestors, EmptyCl); + + return fixed_point1(I, J, Ancestors, Sloop, Sij,flag(Opt->index_flat)); + } + else if(flag(Opt->cycle2)){ + printf("============= Cycle2 ============ \n"); + Plist Si = look_by_rank2(all_clauses, I,flag(Opt->index_flat)); + Si = plist_subtract(Si, EmptyCl); + + return fixed_point2(I, J, Si, Sij, Ancestors); + } + else { + fatal_error("fixed_point : neither cycle1 nor cycle2 is set "); + } + + + + + } + + /************************************************ End Modif ****************************/ + /************* * * search() @@ -2635,115 +3221,202 @@ void basic_clause_properties(Clist sos, Clist usable) */ /* PUBLIC */ -Prover_results search(Prover_input p) -{ - int return_code = setjmp(Jump_env); - if (return_code != 0) { - // we just landed from longjmp(); fix return code and return - print_separator(stdout, "end of search", TRUE); - Glob.return_code = (return_code == INT_MAX ? 0 : return_code); - fatal_setjmp(); /* This makes longjmps cause a fatal_error. */ - return collect_prover_results(p->xproofs); - } - else { - // search for a proof - - print_separator(stdout, "PROCESS INITIAL CLAUSES", TRUE); - - Opt = p->options; // put options into a global variable - Glob.initialized = TRUE; // this signifies that Glob is being used - - Glob.start_time = user_seconds(); - Glob.start_ticks = bogo_ticks(); - - if (flag(Opt->sort_initial_sos) && plist_count(p->sos) <= 100) - p->sos = sort_plist(p->sos, - (Ordertype (*)(void*, void*)) clause_compare_m4); - - // Move clauses and term lists into Glob; do not assign IDs to clauses. - - Glob.usable = move_clauses_to_clist(p->usable, "usable", FALSE); - Glob.sos = move_clauses_to_clist(p->sos, "sos", FALSE); - Glob.demods = move_clauses_to_clist(p->demods,"demodulators",FALSE); - Glob.hints = move_clauses_to_clist(p->hints, "hints", FALSE); - - Glob.weights = tlist_copy(p->weights); - Glob.kbo_weights = tlist_copy(p->kbo_weights); - Glob.actions = tlist_copy(p->actions); - Glob.interps = tlist_copy(p->interps); - Glob.given_selection = tlist_copy(p->given_selection); - Glob.keep_rules = tlist_copy(p->keep_rules); - Glob.delete_rules = tlist_copy(p->delete_rules); - - // Allocate auxiliary clause lists. - - Glob.limbo = clist_init("limbo"); - Glob.disabled = clist_init("disabled"); - Glob.empties = NULL; - - if (flag(Opt->print_initial_clauses)) { - printf("\n%% Clauses before input processing:\n"); - fwrite_clause_clist(stdout, Glob.usable, CL_FORM_STD); - fwrite_clause_clist(stdout, Glob.sos, CL_FORM_STD); - fwrite_clause_clist(stdout, Glob.demods, CL_FORM_STD); - if (Glob.hints->length > 0) - printf("\n%% %d hints input.\n", Glob.hints->length); - } - - // Predicate elimination (may add to sos and move clauses to disabled) - - if (flag(p->options->predicate_elim) && clist_empty(Glob.usable)) { - print_separator(stdout, "PREDICATE ELIMINATION", TRUE); - predicate_elimination(Glob.sos, Glob.disabled, !flag(Opt->quiet)); - print_separator(stdout, "end predicate elimination", TRUE); - } - - basic_clause_properties(Glob.sos, Glob.usable); - - // Possible special treatment for denials (negative in Horn sets) - - if (flag(Opt->auto_denials)) - auto_denials(Glob.sos, Glob.usable, Opt); - - init_search(); // init clocks, ordering, auto-mode, init packages - - index_and_process_initial_clauses(); - - print_separator(stdout, "SEARCH", TRUE); - - printf("\n%% Starting search at %.2f seconds.\n", user_seconds()); - fflush(stdout); - Glob.start_time = user_seconds(); - Glob.searching = TRUE; - - // ****************************** Main Loop ****************************** - - while (inferences_to_make()) { - - // make_inferences: each inferred clause is cl_processed, which - // does forward demodulation and subsumption; if the clause is kept - // it is put on the Limbo list, and it is indexed so that it can be - // used immediately with subsequent newly inferred clauses. - - make_inferences(); - - // limbo_process: this applies back subsumption, back demodulation, - // and other operations that can disable clauses. Limbo clauses - // are moved to the Sos list. - - limbo_process(FALSE); - - } // ************************ end of main loop ************************ - - fprint_all_stats(stdout, Opt ? stringparm1(Opt->stats) : "lots"); - print_separator(stdout, "end of search", TRUE); - fatal_setjmp(); /* This makes longjmps cause a fatal_error. */ - Glob.return_code = SOS_EMPTY_EXIT; - return collect_prover_results(p->xproofs); - } -} /* search */ - -/************* + Prover_results search(Prover_input p) + { + /*********************Modif********************/ + Glob.admissible = TRUE; // At the begining the class is admissible + Glob.rank_emptycl = NULL; + Glob.number_of_calls = 0; + Glob.current_rank = 0; + //Glob.rank_emptycl = get_plist(); + int return_code = setjmp(Jump_env); + if (return_code != 0) { + // we just landed from longjmp(); fix return code and return + print_separator(stdout, "end of search", TRUE); + Glob.return_code = (return_code == INT_MAX ? 0 : return_code); + fatal_setjmp(); /* This makes longjmps cause a fatal_error. */ + return collect_prover_results(p->xproofs); + } + else { + // search for a proof + + print_separator(stdout, "PROCESS INITIAL CLAUSES", TRUE); + + Opt = p->options; // put options into a global variable + Glob.initialized = TRUE; // this signifies that Glob is being used + + Glob.start_time = user_seconds(); + Glob.start_ticks = bogo_ticks(); + + if (flag(Opt->sort_initial_sos) && plist_count(p->sos) <= 100) + p->sos = sort_plist(p->sos, + (Ordertype (*)(void*, void*)) clause_compare_m4); + + // Move clauses and term lists into Glob; do not assign IDs to clauses. + + Glob.usable = move_clauses_to_clist(p->usable, "usable", FALSE); + Glob.sos = move_clauses_to_clist(p->sos, "sos", FALSE); + Glob.demods = move_clauses_to_clist(p->demods,"demodulators",FALSE); + Glob.hints = move_clauses_to_clist(p->hints, "hints", FALSE); + + Glob.weights = tlist_copy(p->weights); + Glob.kbo_weights = tlist_copy(p->kbo_weights); + Glob.actions = tlist_copy(p->actions); + Glob.interps = tlist_copy(p->interps); + Glob.given_selection = tlist_copy(p->given_selection); + Glob.keep_rules = tlist_copy(p->keep_rules); + Glob.delete_rules = tlist_copy(p->delete_rules); + + // Allocate auxiliary clause lists. + + Glob.limbo = clist_init("limbo"); + Glob.disabled = clist_init("disabled"); + Glob.empties = NULL; + + if (flag(Opt->print_initial_clauses)) { + printf("\n%% Clauses before input processing:\n"); + fwrite_clause_clist(stdout, Glob.usable, CL_FORM_STD); + fwrite_clause_clist(stdout, Glob.sos, CL_FORM_STD); + fwrite_clause_clist(stdout, Glob.demods, CL_FORM_STD); + if (Glob.hints->length > 0) + printf("\n%% %d hints input.\n", Glob.hints->length); + } + + // Predicate elimination (may add to sos and move clauses to disabled) + + if (flag(p->options->predicate_elim) && clist_empty(Glob.usable)) { + print_separator(stdout, "PREDICATE ELIMINATION", TRUE); + predicate_elimination(Glob.sos, Glob.disabled,!flag(Opt->quiet)); + print_separator(stdout, "end predicate elimination", TRUE); + } + + basic_clause_properties(Glob.sos, Glob.usable); + + // Possible special treatment for denials (negative in Horn sets) + + if (flag(Opt->auto_denials)) + auto_denials(Glob.sos, Glob.usable, Opt); + + init_search(); // init clocks, ordering, auto-mode, init packages + + index_and_process_initial_clauses(); + + print_separator(stdout, "SEARCH", TRUE); + + printf("\n%% Starting search at %.3f seconds.\n", user_seconds()); + fflush(stdout); + Glob.start_time = user_seconds(); + Glob.searching = TRUE; + + // ****************************** Main Loop ****************************** + + Glob.incr=0; + Glob.max_rank=-1; + BOOL Cycle = TRUE; + Glob.loop=FALSE; + init_tab_rank(Glob.tab_rank); + while (inferences_to_make() && Cycle) { + + // make_inferences: each inferred clause is cl_processed, which + // does forward demodulation and subsumption; if the clause is kept + // it is put on the Limbo list, and it is indexed so that it can be + // used immediately with subsequent newly inferred clauses. + + + /*...................Modif...............*/ + + make_inferences(); + if (flag(Opt->superind)) { + Glob.max_rank = compute_rank_max(Glob.tab_rank); + printf(" max_rank = %d \n", Glob.max_rank); + if(Glob.loop){ + if (get_rank(Glob.loop_clause) <= Glob.max_rank) { + Cycle = FALSE; + p_clause(Glob.loop_clause); + printf("that s a cycle \n"); + printf(" max_rank = %d \n", Glob.max_rank); + } + } + } + // -proo_process: this applies back subsumption, back demodulation, + // and other operations that can disable clauses. Limbo clauses + // are moved to the Sos list. + + limbo_process(FALSE); + if (flag(Opt->superind)) { + if(Glob.ind_empty_clause && Glob.max_rank >= 1 ){ + printf("Induction rule applied to the first parameter clause \n"); + handle_proof_and_maybe_exit2(); + } + if(Glob.max_rank > parm(Opt->start_rank) && !Glob.ind_empty_clause){ // if level empty clauses of rank >= 2 are generated and no empty clause of the forme (N(s^(i)(X)) is generated + BOOL B = TRUE; + printf(" max_rank = %d ", Glob.max_rank ); + int i; + int j; + //int i = rand_i_j(1,Glob.max_rank); + //printf(" i = %d ", i); + //Cycle=FALSE; + //Plist limb = copy_clist_to_plist_shallow(Glob.limbo); + //p_plist(limb); + //Plist dis = copy_clist_to_plist_shallow(Glob.disabled); + //p_plist(dis); + //int j =rand_i_j(2,Glob.max_rank+1); + //printf(" i == %d j== %d \n", i ,j); + //B=fixed_point_without_empties(i, j, Glob.sos, Glob.usable); + if (flag(Opt->random_loopdet)) { + i = rand_i_j(1,Glob.max_rank); + //printf(" i = %d ", i) + j =rand_i_j(i+1,Glob.max_rank+1); + printf(" i == %d j== %d \n", i ,j); + B=fixed_point(i, j, Glob.sos, Glob.usable); + if (B) { + handle_proof_and_maybe_exit2(); + printf(" It's a cycle \n" ); + //handle_proof_and_maybe_exit2(); + Cycle=FALSE; + break; + } + } + else{ + for (i=0; i < Glob.max_rank; i++) {// Check every cycle between i and j + for (j=i+1; j<= Glob.max_rank ; j++) { + printf(" i == %d j== %d \n", i ,j); + B=fixed_point(i, j, Glob.sos, Glob.usable); + if (B) { + handle_proof_and_maybe_exit2(); + printf(" It's a cycle \n" ); + //handle_proof_and_maybe_exit2(); + Cycle=FALSE; + break; + } + } + + } + } + + } + } + + } // ************************ end of main loop ************************ + if (flag(Opt->superind)) { + if (!Cycle) { + handle_proof_and_maybe_exit2(); + } + else { + printf(" End Generation \n"); + + + } + } + fprint_all_stats(stdout, Opt ? stringparm1(Opt->stats) : "lots"); + print_separator(stdout, "end of search", TRUE); + fatal_setjmp(); /* This makes longjmps cause a fatal_error. */ + Glob.return_code = SOS_EMPTY_EXIT; + return collect_prover_results(p->xproofs); + } + } /* search */ + + /************* * * forking_search() * @@ -2994,3 +3667,13 @@ Prover_results forking_search(Prover_input input) return results; } /* end of parent code */ } /* forking_search */ + + /********************* MODIF *****************************/ + + // On suppose abinary_resolution) || + flag(Opt->neg_binary_resolution) || + flag(Opt->pos_hyper_resolution) || + flag(Opt->neg_hyper_resolution) || + flag(Opt->pos_ur_resolution) || + flag(Opt->neg_ur_resolution)); + + // Allocate and initialize indexes (even if they won't be used). + + init_literals_index(); // fsub, bsub, fudel, budel, ucon + + init_demodulator_index(DISCRIM_BIND, ORDINARY_UNIF, 0); + + init_back_demod_index(FPA, ORDINARY_UNIF, 10); + + Glob.clashable_idx = lindex_init(FPA, ORDINARY_UNIF, 10, + FPA, ORDINARY_UNIF, 10); + + init_hints(ORDINARY_UNIF, Att.bsub_hint_wt, + flag(Opt->collect_hint_labels), + flag(Opt->back_demod_hints), + demodulate_clause); + init_semantics(Glob.interps, Clocks.semantics, + stringparm1(Opt->multiple_interps), + parm(Opt->eval_limit), + parm(Opt->eval_var_limit)); + + // Do Sos and Denials last, in case we PROCESS_INITIAL_SOS. + + //////////////////////////////////////////////////////////////////////////// + // Usable + + for (p = Glob.usable->first; p != NULL; p = p->next) { + Topform c = p->c; + //init_ancestors_topform(c); + assign_clause_id(c); + mark_maximal_literals(c->literals); + mark_selected_literals(c->literals, stringparm1(Opt->literal_selection)); + if (flag(Opt->dont_flip_input)) + orient_equalities(c, FALSE); // mark, but don't allow flips + else + c = orient_input_eq(c); /* this replaces c if any flipping occurs */ + index_literals(c, INSERT, Clocks.index, FALSE); + index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); + index_clashable(c, INSERT); + } + + //////////////////////////////////////////////////////////////////////////// + // Demodulators + + if (!clist_empty(Glob.demods) && !flag(Opt->eval_rewrite)) { + fflush(stdout); + bell(stderr); + fprintf(stderr, + "\nWARNING: The use of input demodulators is not well tested\n" + "and discouraged. You might need to clear(process_initial_sos)\n" + "so that sos clauses are not rewritten and deleted.\n"); + fflush(stderr); + } + + for (p = Glob.demods->first; p != NULL; p = p->next) { + Topform c = p->c; + assign_clause_id(c); + if (flag(Opt->eval_rewrite)) { + if (c->is_formula) { + /* make it into a pseudo-clause */ + c->literals = new_literal(TRUE, formula_to_term(c->formula)); + upward_clause_links(c); + zap_formula(c->formula); + c->formula = NULL; + c->is_formula = FALSE; + clause_set_variables(c, MAX_VARS); + mark_oriented_eq(c->literals->atom); + } + } + else { + if (!pos_eq_unit(c->literals)) + fatal_error("input demodulator is not equation"); + else { + int type; + if (flag(Opt->dont_flip_input)) + orient_equalities(c, FALSE); /* don't allow flips */ + else + c = orient_input_eq(c); /* this replaces c if any flipping occurs */ + if (c->justification->next != NULL) { + printf("\nNOTE: input demodulator %d has been flipped.\n", c->id); + fflush(stdout); + fprintf(stderr, "\nNOTE: input demodulator %d has been flipped.\n", + c->id); + if (flag(Opt->bell)) + bell(stderr); + fflush(stderr); + } + type = demodulator_type(c, + parm(Opt->lex_dep_demod_lim), + flag(Opt->lex_dep_demod_sane)); + if (flag(Opt->dont_flip_input) && + type != ORIENTED && + !renamable_flip_eq(c->literals->atom)) { + type = ORIENTED; /* let the user beware */ + mark_oriented_eq(c->literals->atom); + bell(stderr); + fprintf(stderr,"\nWARNING: demodulator does not satisfy term order\n"); + fflush(stderr); + printf("\nWARNING: demodulator does not satisfy term order: "); + f_clause(c); + fflush(stdout); + } + else if (type == NOT_DEMODULATOR) { + Term a = ARG(c->literals->atom,0); + Term b = ARG(c->literals->atom,1); + printf("bad input demodulator: "); f_clause(c); + if (term_ident(a, b)) + fatal_error("input demodulator is instance of x=x"); + else if (!variables_subset(a, b) && !variables_subset(b, a)) + fatal_error("input demoulator does not have var-subset property"); + else + fatal_error("input demoulator not allowed"); + } + index_demodulator(c, type, INSERT, Clocks.index); + } + } + } + + if (flag(Opt->eval_rewrite)) + init_dollar_eval(Glob.demods); + + //////////////////////////////////////////////////////////////////////////// + // Hints + + if (Glob.hints->first) { + for (p = Glob.hints->first; p != NULL; p = p->next) { + Topform h = p->c; + // assign_clause_id(h); // This should be optional + orient_equalities(h, TRUE); + renumber_variables(h, MAX_VARS); + index_hint(h); + } + } + + //////////////////////////////////////////////////////////////////////////// + // Sos + + // Move Sos to a temporary list, then process that temporary list, + // putting the clauses back into Sos in the "correct" way, either + // by calling cl_process() or doing it here. + + temp_sos = Glob.sos; // move Sos to a temporary list + name_clist(temp_sos, "temp_sos"); // not really necessary + Glob.sos = clist_init("sos"); // get a new (empty) Sos list + + if (flag(Opt->process_initial_sos)) { + + if (flag(Opt->print_initial_clauses)) + printf("\n"); + /*********************************** Modif **************************/ + Topform schema;// the (alpha,C)-clause + int unit_loop = 0; // unit_loop is the number of (alpha,C)-clauses + while (temp_sos->first) { + Topform c = temp_sos->first->c; + if (!param_free(c)) {// + unit_loop ++;// + if (unit_loop == 1) {// + + schema = c;// + printf("Loop1"); p_clause(schema); + } + } + Topform new; + clist_remove(c, temp_sos); + clist_append(c, Glob.disabled); + + new = copy_inference(c); // c has no ID, so this is tricky + cl_process_simplify(new); + if (new->justification->next == NULL) { + // No simplification occurred, so make it a clone of the parent. + zap_just(new->justification); + new->justification = copy_justification(c->justification); + // Get all attributes, not just inheritable ones. + zap_attributes(new->attributes); + new->attributes = copy_attributes(c->attributes); + } + else { + // Simplification occurs, so make it a child of the parent. + assign_clause_id(c); + new->justification->u.id = c->id; + if (flag(Opt->print_initial_clauses)) { + printf(" "); + fwrite_clause(stdout, c, CL_FORM_STD); + } + } + cl_process(new); // This re-simplifies, but that's ok. + } + /********************************* Modif ********************** */ + /* if (unit_loop == 1) {// if there is only one (alpha,c)-clause of the form N(X) | p(X) + printf("Loop2"); p_clause(schema); + + Topform Newc = build_loop_clause(schema);//we add a new clause of the form N(s(X)) | p(X) + printf("Loop\n"); + Glob.SI = plist_append(NULL, schema); + Glob.SIJ = plist_append(NULL, Newc); + Glob.ind_empty_clause = TRUE; + + }*/ + + + // This will put processed clauses back into Sos. + limbo_process(TRUE); // back subsumption and back demodulation. + + } + else { + /* not processing initial sos */ + fflush(stdout); + bell(stderr); + fprintf(stderr, + "\nWARNING: clear(process_initial_sos) is not well tested.\n" + "We usually recommend against using it.\n"); + fflush(stderr); + + /* not applying full processing to initial sos */ + while (temp_sos->first) { + Topform c = temp_sos->first->c; + clist_remove(c, temp_sos); + + if (number_of_literals(c->literals) == 0) + /* in case $F is in input, or if predicate elimination finds proof */ + handle_proof_and_maybe_exit(c); + else { + assign_clause_id(c); + if (flag(Opt->dont_flip_input)) + orient_equalities(c, FALSE); + else + c = orient_input_eq(c); + mark_maximal_literals(c->literals); + mark_selected_literals(c->literals, + stringparm1(Opt->literal_selection)); + c->weight = clause_weight(c->literals); + if (!clist_empty(Glob.hints)) { + clock_start(Clocks.hints); + adjust_weight_with_hints(c, + flag(Opt->degrade_hints), + flag(Opt->breadth_first_hints)); + clock_stop(Clocks.hints); + } + + c->initial = TRUE; + insert_into_sos2(c, Glob.sos); + printf("KK"); + //index_literals(c, INSERT, Clocks.index, FALSE); + index_back_demod(c, INSERT, Clocks.index, flag(Opt->back_demod)); + } + } + } + + clist_zap(temp_sos); // free the temporary list + + //////////////////////////////////////////////////////////////////////////// + // Print + + print_separator(stdout, "end of process initial clauses", TRUE); + + print_separator(stdout, "CLAUSES FOR SEARCH", TRUE); + + if (flag(Opt->print_initial_clauses)) { + printf("\n%% Clauses after input processing:\n"); + fwrite_clause_clist(stdout,Glob.usable, CL_FORM_STD); + fwrite_clause_clist(stdout,Glob.sos, CL_FORM_STD); + fwrite_demod_clist(stdout,Glob.demods, CL_FORM_STD); + } + if (Glob.hints->length > 0) { + int redundant = redundant_hints(); + printf("\n%% %d hints (%d processed, %d redundant).\n", + Glob.hints->length - redundant, Glob.hints->length, redundant); + } + + print_separator(stdout, "end of clauses for search", TRUE); + + } // index_and_process_initial_clauses + diff --git a/stab.in b/stab.in new file mode 100644 index 0000000..af292f1 --- /dev/null +++ b/stab.in @@ -0,0 +1,28 @@ +%\/i=1..n p_i /\i=1..n -p_i +% From Regstab +% Unsat +%assign(max_weight, 500). +set(breadth_first). +set(prolog_style_variables). +assign(max_given, 100). +set(raw). +%set(ordered_res). +set(ur_resolution). +set(binary_resolution). +assign(order, kbo). +%assign(literal_selection, none). +clear(predicate_elim). + +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). + S1(0) <-> -P(0) . +S1(s(X)) <-> (S1(X) | P(X)) . + N(X) | S1(X) . +%-P(X). + S2(0) <-> P(0) . + S2(s(X)) <-> (S2(X) & -P(X)) . + N(X) | S2(X) . +end_of_list. \ No newline at end of file diff --git a/stab1.in b/stab1.in new file mode 100644 index 0000000..8e05f4d --- /dev/null +++ b/stab1.in @@ -0,0 +1,16 @@ +% X + 0 = X +% unsat OK +assign(max_weight, 15). + set(prolog_style_variables). + assign(max_given, 300). + set(raw). + set(binary_resolution). + assign(order, kbo). + assign(literal_selection, none). + clear(predicate_elim). + list(kbo_weights). + s = 3. + end_of_list. + formulas(sos). +(( S1(0) <-> ( ((S(0) <-> ( - ( ( - (A(0) <-> B(0) ) ) <-> C(0))) ) & (C(s(0)) <-> (A(0) & B(0) | C(0) & A(0) | C(0) & B(0)))) ) ) & ( S1(s(X)) <-> ( S1(X) & ( ((S(X) <-> ( - ( ( - (A(X) <-> B(X) ) ) <-> C(X))) ) & (C(s(X)) <-> (A(X) & B(X) | C(X) & A(X) | C(X) & B(X)))) ) ) ) & ( N(X) | S1(X) ) & -C(0) & ( S2(0) <-> -B(0) ) & ( S2(s(X)) <-> ( S2(X) & -B(X) ) ) & ( N(X) | S2(X) ) & ( S3(0) <-> ( ( - (A(0) <-> S(0)) ) ) ) & ( S3(s(X)) <-> ( S3(X) | ( ( - (A(X) <-> S(X)) ) ) ) ) & ( N(X) | S3(X) ) ) . +end_of_list. \ No newline at end of file diff --git a/stab2.in b/stab2.in new file mode 100644 index 0000000..3e8fe6a --- /dev/null +++ b/stab2.in @@ -0,0 +1,14 @@ +assign(max_weight, 15). + set(prolog_style_variables). + assign(max_given, 100). + set(raw). + set(binary_resolution). + assign(order, kbo). + assign(literal_selection, none). + clear(predicate_elim). + list(kbo_weights). + s = 3. + end_of_list. + formulas(sos). +( S1(0) <-> ( ((S(0) <-> ( - ( ( - (A(0) <-> B(0) ) ) <-> C(0)) ) ) ) ) & ( S1(s(X)) <-> ( S1(X) & ( ((S(X) <-> ( - ( ( - (A(X) <-> B(X) ) ) <-> C(X)) ) ) ) ) ) & ( N(X) | S1(X) ) ) & (C_i+1 <-> (A_i & B_i | C_i & A_i | C_i & B_i))) & -C_1 & ( S2(0) <-> -B(0) ) & ( S2(s(X)) <-> ( S2(X) & -B(X) ) ) & ( N(X) | S2(X) ) & ( S3(0) <-> ( ( - (A(0) <-> S(0)) ) ) ) & ( S3(s(X)) <-> ( S3(X) | ( ( - (A(X) <-> S(X)) ) ) ) ) & ( N(X) | S3(X) ) . +end_of_list. \ No newline at end of file diff --git a/x1.doc b/x1.doc new file mode 100644 index 0000000..0befbd5 Binary files /dev/null and b/x1.doc differ diff --git a/x1.rtf b/x1.rtf new file mode 100644 index 0000000..cf972a4 --- /dev/null +++ b/x1.rtf @@ -0,0 +1,13 @@ +{\rtf1\ansi\ansicpg1252\cocoartf1038\cocoasubrtf360 +{\fonttbl\f0\fswiss\fcharset0 Helvetica;} +{\colortbl;\red255\green255\blue255;} +\paperw11900\paperh16840\margl1440\margr1440\vieww9000\viewh8400\viewkind0 +\pard\tx566\tx1133\tx1700\tx2267\tx2834\tx3401\tx3968\tx4535\tx5102\tx5669\tx6236\tx6803\ql\qnatural\pardirnatural + +\f0\fs24 \cf0 formulas(sos).\ + \ + P(0,a).\ + -P(x,y) | P(s(x),f(y)).\ + n!=x | -P(x,y) .\ + \ +end_of_list.} \ No newline at end of file diff --git a/x10serie.in b/x10serie.in new file mode 100644 index 0000000..101ed80 --- /dev/null +++ b/x10serie.in @@ -0,0 +1,25 @@ +assign(max_weight, 30). +%set(raw). +set(print_gen). +assign(order, kbo). +set(binary_resolution). +clear(neg_binary_resolution). +assign(literal_selection, none). +clear(predicate_elim). +predicate_order([N,!=,=]). +list(kbo_weights). + s = 3. +end_of_list. +formulas(sos). + f(0,r)=1. + minus(1)=0. + f(s(x),r)=r*f(x,r). + sigma(0) = q. + sigma(s(x))=sigma(x)+(f(x,r)*q). + N(s(x)) | sigma(x)*minus(q) != q*minus(f(s(x),r)) . + + +end_of_list. + + + diff --git a/x11somme.in b/x11somme.in new file mode 100644 index 0000000..82bc8c2 --- /dev/null +++ b/x11somme.in @@ -0,0 +1,31 @@ +assign(max_weight, 30). +%set(raw). +%set(print_gen). +assign(order, kbo). +assign(max_given, 100). +set(binary_resolution). +clear(neg_binary_resolution). +assign(literal_selection, none). +clear(predicate_elim). +%predicate_order([N,=]). +list(kbo_weights). + s = 3. +end_of_list. +formulas(sos). + X+Y=Y+X. + X*Y=Y*X. + X*1=X. + 1+X=s(X). +%s(0)=1. +%s(X)=X+1. + sigma(1)=1. +minus(X,X)=0. +minus(X+Y,Y)=X. +2*minus(X,Y)=minus(2*X,2*Y). +minus(sigma(s(X)),s(X))=sigma(X). + N(X) | 2*sigma(X) != X*s(X) . + + +end_of_list. + + diff --git a/x12Fur.in b/x12Fur.in new file mode 100644 index 0000000..95ee3ac --- /dev/null +++ b/x12Fur.in @@ -0,0 +1,27 @@ +assign(max_weight, 100). +set(prolog_style_variables). +set(raw). +set(binary_resolution). +set(ordered_res). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +op(700, infix,"!=" ). +op(700, infix,"<" ). +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). +-R(s(X)) | R(X). + 0 < t(S). + R� . % r � partir du quel R est faux +fs(S) | -(1 < 1+(t(S)*X)) | fs1(S,S,X). +0 < X * Y | 0 < Y | 0 < X. + R(S1) | -fs1(S1,S,X). % fs1(S,X) est vide si S>r + -R(S1) | -fs1(S1,S,X) | p(s(S1)) * s4(1+(t(S)*X))= 1+(t(S) * X ) | fs1(s(S1),S,X). +N(S) | -fs(S). + +end_of_list. + + diff --git a/x13Prop1.in b/x13Prop1.in new file mode 100644 index 0000000..cf5b140 --- /dev/null +++ b/x13Prop1.in @@ -0,0 +1,22 @@ +% UNSAT OK +assign(max_weight, 100). +set(prolog_style_variables). +set(raw). +set(binary_resolution). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). +p(0). +-p(X) | q(X). +-q(X) | -q(s(X)). +q(X) | q(s(X)). +N(X) |-q(X). +N(X) | -q(s(X)). +end_of_list. + + diff --git a/x14RegStabAdd1.in b/x14RegStabAdd1.in new file mode 100644 index 0000000..23c55f1 --- /dev/null +++ b/x14RegStabAdd1.in @@ -0,0 +1,25 @@ +% Unsat OK +% X + 0 = X. +assign(max_weight, 15). +set(prolog_style_variables). +assign(max_given, 100). +set(raw). +set(binary_resolution). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). + +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). +(p(X) <-> ( -(-(a(X)<->b(X)) <-> c(X)) )) & (c(s(X)) <-> ((a(X) & b(X)) | (c(X) & a(X)) |(c(X) & b(X))) ). +-c(0). +-b(X). +q(0) <-> -(a(0) <-> p(0)). +q(s(X)) <-> (q(X) | -(a(X) <-> p(X)) ). +N(X) | q(X). +end_of_list. + + diff --git a/x15.in b/x15.in new file mode 100644 index 0000000..1e31807 --- /dev/null +++ b/x15.in @@ -0,0 +1,14 @@ +set(prolog_style_variables). +clear(predicate_elim). +set(raw). +set(binary_resolution). +set(print_gen). +assign(max_given, 10). +formulas(sos). +p(0,f(a,b)). +-p(X,f(Y,Z)) | p(s(X),f(Z,Y)) | p(s(X),f(Y,Z)). +N(X) | -p(X,f(a,Z)) . +N(X) | -p(X,f(Z,a)) . +end_of_list. + + diff --git a/x16AssRC.txt b/x16AssRC.txt new file mode 100644 index 0000000..930b81a --- /dev/null +++ b/x16AssRC.txt @@ -0,0 +1,32 @@ +assign(max_weight, 15). + set(prolog_style_variables). + assign(max_given, 100). + set(raw). + set(binary_resolution). + assign(order, kbo). + assign(literal_selection, none). + clear(predicate_elim). + list(kbo_weights). + s = 3. + end_of_list. + formulas(sos). +( S1(0) <-> ( ( B1(0) <-> ( - ( ( - (A1(0) <-> A2(0) ) ) <-> C1(0)) ) & C1(s(0)) <-> (A1(0) & A2(0) | C1(0) & A1(0) | C1(0) & A2(0)) ) ) ) . +( S1(s(X)) <-> ( S1(X) & ( ( B1(X) <-> ( - ( ( - (A1(X) <-> A2(X) ) ) <-> C1(X)) ) & C1(s(X)) <-> (A1(X) & A2(X) | C1(X) & A1(X) | C1(X) & A2(X)) ) ) ) ) . +( N(X) | - S1(X) ) . +-C1(0) . +( S2(0) <-> ( ( S(0) <-> ( - ( ( - (B1(0) <-> A3(0) ) ) <-> C1'(0)) ) & C1'(s(0)) <-> (B1(0) & A3(0) | C1'(0) & B1(0) | C1'(0) & A3(0)) ) ) ) . +( S2(s(X)) <-> ( S2(X) & ( ( S(X) <-> ( - ( ( - (B1(X) <-> A3(X) ) ) <-> C1'(X)) ) & C1'(s(X)) <-> (B1(X) & A3(X) | C1'(X) & B1(X) | C1'(X) & A3(X)) ) ) ) ) . +( N(X) | - S2(X) ) . +-C1'(0) . +( S3(0) <-> ( ( S'(0) <-> ( - ( ( - (A1(0) <-> B2(0) ) ) <-> C2'(0)) ) & C2'(s(0)) <-> (A1(0) & B2(0) | C2'(0) & A1(0) | C2'(0) & B2(0)) ) ) ) . +( S3(s(X)) <-> ( S3(X) & ( ( S'(X) <-> ( - ( ( - (A1(X) <-> B2(X) ) ) <-> C2'(X)) ) & C2'(s(X)) <-> (A1(X) & B2(X) | C2'(X) & A1(X) | C2'(X) & B2(X)) ) ) ) ) . +( N(X) | - S3(X) ) . +-C2'(0) . +( S4(0) <-> ( ( B2(0) <-> ( - ( ( - (A2(0) <-> A3(0) ) ) <-> C2(0)) ) & C2(s(0)) <-> (A2(0) & A3(0) | C2(0) & A2(0) | C2(0) & A3(0)) ) ) ) . +( S4(s(X)) <-> ( S4(X) & ( ( B2(X) <-> ( - ( ( - (A2(X) <-> A3(X) ) ) <-> C2(X)) ) & C2(s(X)) <-> (A2(X) & A3(X) | C2(X) & A2(X) | C2(X) & A3(X)) ) ) ) ) . +( N(X) | - S4(X) ) . +-C2(0) . +( S5(0) <-> ( ( - (S(0) <-> S'(0)) ) ) ) . +( S5(s(X)) <-> ( S5(X) | ( ( - (S(X) <-> S'(X)) ) ) ) ) . +( N(X) | - S5(X) ) . +end_of_list. \ No newline at end of file diff --git a/x17adder4ripplecarry.in b/x17adder4ripplecarry.in new file mode 100644 index 0000000..6b78b9a --- /dev/null +++ b/x17adder4ripplecarry.in @@ -0,0 +1,29 @@ +%From Regstab : bitvectors/ripplecarry/Adder4.stab +% Associativity +assign(max_weight, 1550). +set(prolog_style_variables). +assign(max_given, 4500). +%set(raw). +set(ordered_res). +predicate_order([N, A1,A2, A3,B1, B2, C1, C2, C1P, C2P, S1, S2, S3, S4, S, SP, S5]). +set(binary_resolution). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. +formulas(sos). +( ( N(X) | S1(X) ) & -C1(0) ) & ( ( N(X) | S2(X) ) & -C1P(0) ) & ( ( N(X) | S3(X) ) & -C2P(0) ) & ( ( N(X) | S4(X) ) & -C2(0) ) & ( N(X) | S5(X) ) . +S1(0) <-> ( ( B1(0) <-> -( - (A1(0) <-> A2(0) ) <-> C1(0)) ) & ( C1(s(0)) <-> (A1(0) & A2(0) | C1(0) & A1(0) | C1(0) & A2(0)) ) ) . +S1(s(X)) <-> ( S1(X) & ( ( B1(X) <-> -( - (A1(X) <-> A2(X) ) <-> C1(X)) ) & ( C1(s(X)) <-> (A1(X) & A2(X) | C1(X) & A1(X) | C1(X) & A2(X)) ) ) ) . +S2(0) <-> ( ( S(0) <-> -( - (B1(0) <-> A3(0) ) <-> C1P(0)) ) & ( C1P(s(0)) <-> (B1(0) & A3(0) | C1P(0) & B1(0) | C1P(0) & A3(0)) ) ) . +S2(s(X)) <-> ( S2(X) & ( ( S(X) <-> -( - (B1(X) <-> A3(X) ) <-> C1P(X)) ) & ( C1P(s(X)) <-> (B1(X) & A3(X) | C1P(X) & B1(X) | C1P(X) & A3(X)) ) ) ) . +S3(0) <-> ( ( SP(0) <-> -( - (A1(0) <-> B2(0) ) <-> C2P(0)) ) & ( C2P(s(0)) <-> (A1(0) & B2(0) | C2P(0) & A1(0) | C2P(0) & B2(0)) ) ) . +S3(s(X)) <-> ( S3(X) & ( ( SP(X) <-> -( - (A1(X) <-> B2(X) ) <-> C2P(X)) ) & ( C2P(s(X)) <-> (A1(X) & B2(X) | C2P(X) & A1(X) | C2P(X) & B2(X)) ) ) ) . +S4(0) <-> ( ( B2(0) <-> -( - (A2(0) <-> A3(0) ) <-> C2(0)) ) & ( C2(s(0)) <-> (A2(0) & A3(0) | C2(0) & A2(0) | C2(0) & A3(0)) ) ) . +S4(s(X)) <-> ( S4(X) & ( ( B2(X) <-> -( - (A2(X) <-> A3(X) ) <-> C2(X)) ) & ( C2(s(X)) <-> (A2(X) & A3(X) | C2(X) & A2(X) | C2(X) & A3(X)) ) ) ) . +S5(0) <-> - (S(0) <-> SP(0)) . +S5(s(X)) <-> ( S5(X) | - (S(X) <-> SP(X)) ) . + +end_of_list. \ No newline at end of file diff --git a/x18Ceres.in b/x18Ceres.in new file mode 100644 index 0000000..7fd8ceb --- /dev/null +++ b/x18Ceres.in @@ -0,0 +1,40 @@ +assign(max_weight, 14). +set(prolog_style_variables). +assign(max_given, 1200). + +%set(raw). +%set(lightest_first). +%set(print_gen). +%set(back_subsume). +%set(back_demod). +%set(cac_redundancy). +%assign(max_depth, 4). + +%set(ordered_para). +%set(paramodulation). +%set(binary_resolution). + +assign(literal_selection, none). +clear(predicate_elim). +assign(order, kbo). +predicate_order([N,p,g,r,q, =]). +list(kbo_weights). + s = 10. +end_of_list. + +formulas(sos). + +N(X) | q(X). +(r(0) & p(Z)) -> p(f(g(0,Z))). +-q(0). +-r(s(X)) | r(X). +(r(s(X)) & p(g(X,Z )) ) -> p(f(g(X,Z))). +-q(s(X)) | r(s(X)). +-q(s(X)) | p(a). +-(q(s(X)) & p(f(g(X, a))) ). +g(0,Z) = Z. +g(s(X), Z) = f(g(X,Z)). + +end_of_list. + + diff --git a/x18Ceres1.in b/x18Ceres1.in new file mode 100644 index 0000000..82654bd --- /dev/null +++ b/x18Ceres1.in @@ -0,0 +1,38 @@ +assign(max_weight, 14). +set(prolog_style_variables). +assign(max_given, 1200). + +%set(raw). +%set(lightest_first). +%set(print_gen). +%set(back_subsume). +%set(back_demod). +%set(cac_redundancy). +assign(max_depth, 4). + +%set(ordered_para). +%set(paramodulation). +%set(binary_resolution). + +assign(literal_selection, none). +clear(predicate_elim). +assign(order, kbo). +%predicate_order([N,p,g,r,q, =]). +list(kbo_weights). + s = 10. +end_of_list. + +formulas(sos). +(r(0) & p(Z)) -> p(f(g(0,Z))). +-q(0). +-r(s(X)) | r(X). +(r(s(X)) & p(g(X,Z )) ) -> p(f(g(X,Z))). +-q(s(X)) | r(s(X)). +p(a). +-(q(s(X)) & p(f(g(X, a))) ). +g(0,Z) = Z. +g(s(X), Z) = f(g(X,Z)). +N(X) | q(X). +end_of_list. + + diff --git a/x18Ceres1e.in b/x18Ceres1e.in new file mode 100644 index 0000000..d2b7fb7 --- /dev/null +++ b/x18Ceres1e.in @@ -0,0 +1,35 @@ +set(prolog_style_variables). +assign(max_given, 100). + +set(raw). +set(rank_given). +%set(print_gen). +%set(back_subsume). +%set(back_demod). +set(cac_redundancy). +%assign(max_depth, 4). + +set(ordered_res). +%set(paramodulation). +set(binary_resolution). +assign(order, kbo). +assign(literal_selection, none). +clear(predicate_elim). + + + +formulas(sos). +(r(0) & p(Z)) -> p(f(g(0,Z))). +-q(0). +-r(s(X)) | r(X). +(r(s(X)) & p(g(X,Z )) ) -> p(f(g(X,Z))). +-q(s(X)) | r(s(X)). +p(a). +-(q(s(X)) & p(f(g(X, a))) ). +e(g(0,Z), Z). +e(g(s(X), Z), f(g(X,Z)) ). +e(X,X). +N(X) | q(X). +end_of_list. + + diff --git a/x19Complexity_10.in b/x19Complexity_10.in new file mode 100644 index 0000000..57e57a6 --- /dev/null +++ b/x19Complexity_10.in @@ -0,0 +1,28 @@ +% Unsat OK +assign(max_weight, 100). +%assign(max_seconds, 1). +set(raw). +set(back_subsume). +set(back_demod). +set(cac_redundancy). +%clear(auto_inference). +set(prolog_style_variables). +%set(print_gen). +set(binary_resolution). +set(paramodulation). +%clear(ordered_res). +assign(max_given, 40). +assign(literal_selection, none). +%predicate_order([N,>]). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. +formulas(sos). +N(X) | (-e(a,T1,T2,T3,T4,T5,T6,T7,T8,T9) & e(T1, a, T2,T3,T4,T5,T6,T7,T8,T9) & t(X) != f(T1,T2,a,T3,T4,T5,T6,T7,T8,T9) & t(X) != f(T1,T2,T3, a,T4,T5,T6,T7,T8,T9) & t(X) != f(T1,T2,T3,T4,a,T5,T6,T7,T8,T9) & t(X) != f(T1,T2,T3,T4,T5,a,T6,T7,T8,T9) & t(X) != f(T1,T2,T3,T4,T5,T6,a,T7,T8,T9) & t(X) != f(T1,T2,T3,T4,T5,T6,T7,a,T8,T9) & t(X) != f(T1,T2,T3,T4,T5,T6,T7,T8,a,T9) & t(X) != f(T1,T2,T3,T4,T5,T6,T7,T8,T9,a)). + +t(X)!=f(Z,T1,T2,T3,T4,T5,T6,T7,T8,T9) | g(t(X)) = f(T1,Z,T2,T3,T4,T5,T6,T7,T8,T9). +t(s(X)) = g(t(X)). +t(0) = f(a,T1,T2,T3,T4,T5,T6,T7,T8,T9). +end_of_list. + diff --git a/x19Complexity_2.in b/x19Complexity_2.in new file mode 100644 index 0000000..81e09ea --- /dev/null +++ b/x19Complexity_2.in @@ -0,0 +1,28 @@ +% Unsat OK +assign(max_weight, 100). +%assign(max_seconds, 1). +set(raw). +clear(back_subsume). +set(back_demod). +set(cac_redundancy). +%clear(auto_inference). +set(prolog_style_variables). +%set(print_gen). +set(random_given). +set(binary_resolution). +set(paramodulation). +%clear(ordered_res). +assign(max_given, 40). +assign(literal_selection, none). +%predicate_order([N,>]). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. +formulas(sos). +N(X) | (t(X) != f(a,Z) & t(X) != f(Z,a) ). +t(X) != f(Z,Y) | (g(t(X)) = f(Z,Y) | g(t(X)) = f(Y,Z)). +t(s(X)) = g(t(X)). +t(0) = f(a,Z). +end_of_list. + diff --git a/x19Complexity_3.in b/x19Complexity_3.in new file mode 100644 index 0000000..3a6567b --- /dev/null +++ b/x19Complexity_3.in @@ -0,0 +1,30 @@ +% Unsat OK +assign(max_weight, 14). +%assign(max_seconds, 1). +set(raw). +%set(back_subsume). +%set(back_demod). +%set(cac_redundancy). +%clear(auto_inference). +set(prolog_style_variables). +%set(print_gen). +assign(max_depth, 5). +%set(ordered_para). +set(paramodulation). +set(binary_resolution). +%clear(ordered_res). +assign(max_given, 100). +assign(literal_selection, none). +predicate_order([N,!=,=]). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. +formulas(sos). +N(X) | (t(X) != f(a,Z,T) & t(X) != f(Z,a,T) & t(X) != f(Z,T,a)). + +t(X) != f(X1,X2,X3) | (f(X1,X2,X3) = g(t(X)) | f(X2,X1,X3) = g(t(X)) | f(X3,X2,X1) = g(t(X)) | f(X1,X3,X2) = g(t(X)) ). +t(s(X)) = g(t(X)). +t(0) = f(a,Z,T). +end_of_list. + diff --git a/x19Complexity_3e.in b/x19Complexity_3e.in new file mode 100644 index 0000000..05d424d --- /dev/null +++ b/x19Complexity_3e.in @@ -0,0 +1,30 @@ +% Unsat OK +assign(max_weight, 14). +%assign(max_seconds, 1). +set(raw). +set(back_subsume). +set(back_demod). +set(cac_redundancy). +%clear(auto_inference). +set(prolog_style_variables). +set(print_gen). +%set(breadth_first). +assign(order, kbo). +set(random_given). +%set(ordered_para). +%set(paramodulation). +set(binary_resolution). +%clear(ordered_res). +assign(max_given, 1000). +predicate_order([ N, e ]). +assign(literal_selection, none). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. +formulas(sos). +N(X) | (-e(X,a,X2,X3) & -e(X, X2,a,X3 ) & -e(X, X2,X3,a) ). +-e(X, X1,X2,X3) | (e(s(X) ,X1,X2,X3) | e(s(X), X2,X1,X3 ) | e(s(X), X3,X2,X1) | e(s(X) ,X1,X3,X2) ). +e(0, a,b,c). +end_of_list. + diff --git a/x1Triv.in b/x1Triv.in new file mode 100644 index 0000000..cd8a3d4 --- /dev/null +++ b/x1Triv.in @@ -0,0 +1,20 @@ +% Unsat OK +assign(max_weight, 15). +set(raw). +%clear(loopdet). +set(random_given). +set(print_gen). +set(binary_resolution). +%clear(neg_binary_resolution). +assign(literal_selection, none). +%set(hyper_resolution). +set(predicate_elim). +set(input_sos_first). +set(factor). +formulas(sos). + ( N(x) | -P(x,y) ) & (N(s(y)) | P(x,y) | q(x)) & (-P(x,y) | P(s(x),f(y))) & P(0,a) & (q(x) | -q(s(x))). + +end_of_list. + + + diff --git a/x1tab.in b/x1tab.in new file mode 100644 index 0000000..d5d6b4e --- /dev/null +++ b/x1tab.in @@ -0,0 +1,30 @@ +%assign(max_weight, 100). +%set(random_given). +set(prolog_style_variables). +assign(max_given, 60). +%set(raw). +%set(print_gen). +clear(ordered_res). +assign(literal_selection, none). + +%predicate_order([ N,= ]). +clear(predicate_elim). +%set(paramodulation). +%clear(hyper_resolution). +%list(kbo_weights). +% s = 6. + % i = 3. +%end_of_list. + +formulas(sos). +t(0) =tt. + tp(0) = store(tt, ip, a). +t(s(J)) = store(t(J), i(J) , e(J)). +tp(s(J)) = store(tp(J), i(J) , e(J)). +all J (i(J) != ip). +select(store(T, X , V) , X ) = V. +X = Y | select(store(T, X , V) , Y ) = select(T,Y). +N(A) | select(store( t(A), ip , a) , is) != select(tp(A),is) . +end_of_list. + + diff --git a/x20production.in b/x20production.in new file mode 100644 index 0000000..c2feaef --- /dev/null +++ b/x20production.in @@ -0,0 +1,40 @@ +% Unsat OK +assign(max_weight, 100). +%assign(max_seconds, 1). +set(raw). +set(back_subsume). +set(back_demod). +set(cac_redundancy). +%clear(auto_inference). +set(prolog_style_variables). +%set(print_gen). +set(binary_resolution). +set(paramodulation). +%clear(ordered_res). +assign(max_given, 40). +assign(literal_selection, none). +%predicate_order([N,>]). +clear(predicate_elim). +list(kbo_weights). + s = 5. +end_of_list. +formulas(sos). +%Je pense qu'on peut facilement trouver des exemples int�ressants suivant %ce principe, avec pas mal de variations possibles et pouvant �tre %compliqu�es autant qu'on veut. Un exemple tr�s simple: +%p_i(x,y): code le fait que la ressource x est associ�e au client y � %l'instant i +%q(x,y): le fait que le client demande la ressource x +%r_i(x,y): code le fait que la ressource x a d�j� �t� associ�e au client y %(avant l'instant i) + +%On peut consid�rer un nbre arbitraire (mais fix�, sf � consid�rer des %sch�mas avec deux param�tres...) de clients et de ressources. + +%On peut ensuite d�finir une politique d'attribution comme un ensemble de %clauses du premier ordre et utiliser le calcul pour v�rifier ses %propri�t�s. Par exemple, on peut supposer que les clients sont totalement %ordonn�s et que toute ressource r est affect�e en priorit� au client %maximal qui la demande. Puis on v�rifie que tout client finit par obtenir %la ressource qu'il souhaite. +a > b. +b > c. +a > c. +-r(I,R,T) | -q(X,R). +( (X > Z) & q(X,R) & q(Z,R) & -r(I,R,T) ) -> p(I,X,R). +(p(I,X,R) & -q(Z,R) ) -> p(s(I),X,R)). +(p(I,X,R) & (q(Z,R) & X > Z )) -> p(s(I),X,R)). +N(X) | -p(X,Z,R). + +end_of_list. + diff --git a/x2socrate.in b/x2socrate.in new file mode 100644 index 0000000..450cea7 --- /dev/null +++ b/x2socrate.in @@ -0,0 +1,10 @@ + +formulas(sos). + + homme(elias). + -homme(x) | mortel(x). + -mortel(x). + +end_of_list. + +clear(predicate_elim). \ No newline at end of file diff --git a/x4.in b/x4.in new file mode 100644 index 0000000..6f4067c --- /dev/null +++ b/x4.in @@ -0,0 +1,9 @@ +set(prolog_style_variables). + +formulas(sos). +p(0,f(a,b)). +-p(X,f(Y,Z)) | p(s(X),f(Z,Y)) | p(s(X),f(Y,Z)). +N(X) | -p(X,f(a,Z)) . +N(X) | -p(X,f(Z,a)) . +end_of_list. + diff --git a/x6tab.in b/x6tab.in new file mode 100644 index 0000000..fb35e59 --- /dev/null +++ b/x6tab.in @@ -0,0 +1,28 @@ +set(prolog_style_variables). +assign(max_given, 2300). +set(raw). +set(index_flat). +%set(print_gen). +set(superind). +%set(cycle2). +set(rank_given). +assign(start_rank, 1). +set(binary_resolution). +set(ordered_res). +set(paramodulation). +set(back_subsume). +assign(order, kbo). +clear(predicate_elim). +list(kbo_weights). +s = 3. +end_of_list. + +formulas(sos). +t(0) = tz. +t(s(U)) = store(t(U),b(U),c(U)). +-(b(i) = a). +select(t(0), a)=d. +N(U) | select(t(U), a) != d. +x != y | select(store(r, x , v) , y ) = v. +x = y | select(store(r, x , v) , y ) = select(r,y). +end_of_list. diff --git a/x7Fur.in b/x7Fur.in new file mode 100644 index 0000000..0b0b003 --- /dev/null +++ b/x7Fur.in @@ -0,0 +1,33 @@ +% Unsat OK +% ts > 0. +assign(max_given, 100). +%set(raw). +set(binary_resolution). +%set(paramodulation). +assign(order, kbo). +clear(back_subsume). +%clear(neg_binary_resolution). +assign(literal_selection, none). +%assign(literal_selection, max_negative). +%op(700, infix,"!=" ). +%op(700, infix,"<" ). +%predicate_order([N,=,>]). +clear(predicate_elim). + +list(kbo_weights). + s = 3. +end_of_list. + +formulas(sos). +N(x) |-( f(x) > 0). +f(s(x)) = *(f(x),p(x)). +f(0)=1. +p(y) > 1. +1 > 0. +-(x > 1) | x > 0. +-(x>0) | *(1,x) > 0. +*(1,x)=x. +-(x>0) | -(y>0) | x*y > 0. +end_of_list. + + diff --git a/x8ACO.in b/x8ACO.in new file mode 100644 index 0000000..9ced3c0 --- /dev/null +++ b/x8ACO.in @@ -0,0 +1,43 @@ +% Unsat OK +% X1 * � * Xn = Xn * � X1 +%assign(max_weight, 14). +%assign(max_seconds, 1). +%set(raw). +set(random_given). +assign(max_given, 20). +%set(print_gen). +set(binary_resolution). +set(back_subsume). +set(ordered_res). +set(paramodulation). +set(ordered_para). +assign(max_literals, 5). +assign(max_depth, 4). +%set(back_demod). +assign(literal_selection, none). +predicate_order([N,=]). +%clear(process_initial_sos). + +clear(predicate_elim). +list(kbo_weights). + s = 3. +end_of_list. +%formulas(demodulators). + +%*(x,1)=x. +%*(1,x)=x. +%end_of_list. +formulas(sos). +N(x) | p(x) != q(x). +p(s(x)) = p(x)*a(x). +q(s(x)) = a(x)*q(x). +x*y = u*v | x != u | y!=v. +p(0) = 1. +q(0)=1. +*(x,1)=x. +*(1,x)=x. + + +end_of_list. + + diff --git a/x8ACOe.in b/x8ACOe.in new file mode 100644 index 0000000..a00a8bf --- /dev/null +++ b/x8ACOe.in @@ -0,0 +1,53 @@ +assign(max_weight, 30). +set(raw). +%clear(auto_inference). + + +assign(max_given, 180). +assign(order, kbo). +set(raw). +set(ordered_res). +set(breadth_first). +assign(max_literals, 5). +assign(max_depth, 5). +clear(back_subsume). +%assign(max_megs, 1). +set(binary_resolution). +%set(paramodulation). +%clear(pos_hyper_resolution). +%clear(neg_hyper_resolution). +%clear(hyper_resolution). +assign(literal_selection, none). +%predicate_order([N,e,p,q]). +set(predicate_elim). +list(kbo_weights). + s = 25. + e = 2. + p = 3. + q = 4. +end_of_list. +%list(actions). + + % given=50 -> set(random_given). +% given=50 -> set(print_gen). + + +%end_of_list. +formulas(sos). + + +N(x) | -p(x,u) | -q(x,v) | -e(u,v). + +p(s(x),a(x)*y) | -p(x,y). +q(s(x),y*a(x)) | -q(x,y). + +e(x*y,u*v) | -e(x,u) | -e(y,v). +e(x*y,u*v) | -e(x,v) | -e(y,u). +p(0,1). +q(0,1). +e(x,x). +e(x*1,x). +e(x,x*1). +end_of_list. + + diff --git a/x9paire.in b/x9paire.in new file mode 100644 index 0000000..98a2dcb --- /dev/null +++ b/x9paire.in @@ -0,0 +1,22 @@ +% UNSAT NOT YET +assign(max_weight, 15). +%set(raw). +%set(print_gen). +set(binary_resolution). +clear(neg_binary_resolution). +assign(literal_selection, none). +clear(predicate_elim). + +formulas(sos). +p(s(zk),i(y),s(s(x))) | -p(zk,i(y),x). +all wj( p(s(zk),wj , s(s(x))) | -p(zk,wj,x) | wj = i(y)). +p(0,a,b). +even(b). +N(y) | -p(y,a,x) | -even(x). +even(s(s(x))) | -even(x). +-even( s(s(x)) )| even(x). +even(0). +-even(s(0)). +end_of_list. + + diff --git a/xTPTP1.in b/xTPTP1.in new file mode 100644 index 0000000..6f8bb57 --- /dev/null +++ b/xTPTP1.in @@ -0,0 +1,28 @@ +% Unsat OK +assign(max_weight, 100). +%assign(max_seconds, 1). +set(raw). +set(binary_resolution). +%clear(auto_inference). +set(prolog_style_variables). +set(print_gen). +%clear(ordered_res). +assign(max_given, 30). +clear(predicate_elim). +% p(0*). p[0] +% p(x*01*) -> p(x*10*). p[i] -> p[i + 1] +% not p(1*). not p[2^n - 1] + +list(kbo_weights). + s = 3. +end_of_list. +formulas(sos). +N(X) | -p(som(X)) . +p(0). +-p(X) | p(s(X)). +p(som(0)) . +p(som(s(X))) <-> p((2 * som(X)) + 1). + + +end_of_list. + diff --git a/xTPTP1Part1.in b/xTPTP1Part1.in new file mode 100644 index 0000000..1aa3adb --- /dev/null +++ b/xTPTP1Part1.in @@ -0,0 +1,28 @@ +% Unsat OK +assign(max_weight, 100). +%assign(max_seconds, 1). +set(raw). +set(binary_resolution). +%clear(auto_inference). +set(prolog_style_variables). +set(print_gen). +%clear(ordered_res). +assign(max_given, 1000). +clear(predicate_elim). +% p(0*). p[0] +% p(x*01*) -> p(x*10*). p[i] -> p[i + 1] +% not p(1*). not p[2^n - 1] + +list(kbo_weights). + s = 3. +end_of_list. +formulas(sos). + +p(0). +-p(X) | p(s(X)). +p(som(0)) . +p(som(s(X))) <-> p((2 * som(X)) + 1). +exists X (p(som(X)) & -p(som(s(X)))). + +end_of_list. + diff --git a/xTest.in b/xTest.in new file mode 100644 index 0000000..1042582 --- /dev/null +++ b/xTest.in @@ -0,0 +1,31 @@ +% Unsat OK +assign(max_weight, 100). +%assign(max_seconds, 1). +%set(raw). +%clear(auto_inference). +set(prolog_style_variables). +set(print_gen). +set(binary_resolution). +%clear(ordered_res). +assign(max_given, 60). +assign(literal_selection, none). +%predicate_order([N,>]). +clear(predicate_elim). +list(kbo_weights). + s = 3. +end_of_list. +formulas(sos). +N(Y) | -(p(Y) * p(Y) > q(Y)). + +p(s(Y)) = p(Y) + x(Y). +q(s(Y)) = q(Y) + (x(Y) * x(Y)). +p(s(0)) = x(0). +q(s(0)) = x(0) * x(0). +V+Z > V. +V*(Z1 + Z2) = (V*Z1) + (V*Z2). + +*(Y,1)=Y. +*(1,Y)=Y. + +end_of_list. +